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Deck 5: Exponential and Logarithmic Functions
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Question
The concentration of a drug in grams/cubic centimeter (g/cm3) t minutes after it has been injected into the bloodstream is given by 
where w, p, and k are positive constants, with p > w.
At what time is the concentration of the drug the greatest? What will be the concentration of the drug in the long run?
A)
B) 
C) 
D) 
where w, p, and k are positive constants, with p > w. At what time is the concentration of the drug the greatest? What will be the concentration of the drug in the long run?
A)
B)
C)
D)
Question
The length (in centimeters) of a typical Pacific halibut t years old is approximately 
.
What is the length of a typical 5-year-old Pacific halibut? How fast is the length of a typical 5-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?
A) 85.8 cm; 14.5 cm/yr; 202 cm;
B) 115.6 cm; 13.8 cm/yr; 202 cm;
C) 128.7 cm; 0.952 cm/yr; 229 cm;
D) 202.0 cm; 11.7 cm/yr; 256 cm;
.
What is the length of a typical 5-year-old Pacific halibut? How fast is the length of a typical 5-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?
A) 85.8 cm; 14.5 cm/yr; 202 cm;
B) 115.6 cm; 13.8 cm/yr; 202 cm;
C) 128.7 cm; 0.952 cm/yr; 229 cm;
D) 202.0 cm; 11.7 cm/yr; 256 cm;
Question
Question
If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law 
where p0 is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 17 lb/in.2 at sea level and 11.5 lb/in.2 at 5,000 ft, how fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Give the answer to four decimal places.
A) 0.0004 lb/in.2/ft
B) 0.0006 lb/in.2/ft
C) 0.0003 lb/in.2/ft
D) 0.0007 lb/in.2/ft
E) 0.0005 lb/in.2/ft
where p0 is the atmospheric pressure at sea level and k is a constant. If the atmospheric pressure is 17 lb/in.2 at sea level and 11.5 lb/in.2 at 5,000 ft, how fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Give the answer to four decimal places.
A) 0.0004 lb/in.2/ft
B) 0.0006 lb/in.2/ft
C) 0.0003 lb/in.2/ft
D) 0.0007 lb/in.2/ft
E) 0.0005 lb/in.2/ft
Question
Question
The percent of a certain brand of computer chips that will fail after t years of use is estimated to be 
.
What percent of this brand of computer chips are expected to be usable after 6 years?
A) 71.3%
B) 56.7%
C) 69.9%
D) 64.2%
.
What percent of this brand of computer chips are expected to be usable after 6 years?
A) 71.3%
B) 56.7%
C) 69.9%
D) 64.2%
Question
Three hundred students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hours later is given by the function 
.
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours?
A) 1,100
B) 1,085
C) 1,095
D) 1,090
E) 1,080
. If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours?
A) 1,100
B) 1,085
C) 1,095
D) 1,090
E) 1,080
Question
Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by 
.
Select the graph of this function. At what level is the demand expected to stabilize?
A) 
1,900 computers
B) 
1,800 computers
C) 
2,100 computers
D) 
1,800 computers
E) 
1,900 computers
. Select the graph of this function. At what level is the demand expected to stabilize?
A)
1,900 computersB)
1,800 computers C)
2,100 computers D)
1,800 computers E)
1,900 computers Question
Given that a quantity Q(t) exhibiting exponential decay is described by the function 
where t is measured in years. What is the decay constant? What quantity is present initially? Complete the table of values. Round your answer to the nearest integer.
A)
B)
C)
D)
where t is measured in years. What is the decay constant? What quantity is present initially? Complete the table of values. Round your answer to the nearest integer.A)
B)
C)
D)
Question
Phosphorus 32 has a half-life of 14.2 days. If 600 g of this substance are present initially, find the amount present after t days. What amount will be left after 3.55 days? How fast is the phosphorus 32 decaying when t = 3.55?
A)
B)
C) 
D) 
A)
B)
C)
D)
Question
Given that a quantity Q(t) is described by the exponential growth function 
where t is measured in minutes. What is the growth constant? What quantity is present initially? Complete the table of values. Round your answers to the nearest integer. t
A)
B)
C)
D)
where t is measured in minutes. What is the growth constant? What quantity is present initially? Complete the table of values. Round your answers to the nearest integer. tA)
B)
C)
D)
Question
The U.S. population is approximated by the function 
where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 ( t = 3 )?
A) 408.0 millions
B) 322.6 millions
C) 616.3 millions
D) 325.6 millions
where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 ( t = 3 )? A) 408.0 millions
B) 322.6 millions
C) 616.3 millions
D) 325.6 millions
Question
The radioactive element polonium decays according to the law 
where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present?
A) The initial amount was 645 mg
B) The initial amount was 642 mg
C) The initial amount was 651 mg
D) The initial amount was 640 mg
where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present? A) The initial amount was 645 mg
B) The initial amount was 642 mg
C) The initial amount was 651 mg
D) The initial amount was 640 mg
Question
The growth rate of the bacterium, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 20 min. If the initial cell population is 10, determine the function Q(t) that expresses the exponential growth of the number of cells of this bacterium as a function of time t (in minutes). How long will it take for a colony of 10 cells to increase to a population of 1 million? If the initial cell population were 100, how would this alter the model?
A)
B)
C) 
D) 
A)
B)
C)
D)
Question
During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by 
.
How many children were stricken by the flu after the first day? How many children had the flu after 10 days? How many children eventually contracted the disease?
A) 12 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,400 children eventually contracted the disease
B) 15 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,083 children eventually contracted the disease
C) 17 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,246 children eventually contracted the disease
D) 15 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,400 children eventually contracted the disease
. How many children were stricken by the flu after the first day? How many children had the flu after 10 days? How many children eventually contracted the disease?
A) 12 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,400 children eventually contracted the disease
B) 15 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,083 children eventually contracted the disease
C) 17 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,246 children eventually contracted the disease
D) 15 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,400 children eventually contracted the disease
Question
According to estimates by Paul Kroger Associates, the percent of households that own VCRs is given by 
where t is measured in years, with t = 0 corresponding to the beginning of 1985. What percent of households owned VCRs at the beginning of 1985? At the beginning of 1990?
A) 5.0%; 33.6%
B) 5.0%; 34.3%
C) 34.3%; 65.0%
D) 2.9%; 32.9%
where t is measured in years, with t = 0 corresponding to the beginning of 1985. What percent of households owned VCRs at the beginning of 1985? At the beginning of 1990? A) 5.0%; 33.6%
B) 5.0%; 34.3%
C) 34.3%; 65.0%
D) 2.9%; 32.9%
Question
Question
Question
On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model 
where t denotes the number of days since the beginning of the experiment.
How fast was the population changing on the 20th day?
A) 18 flies/day
B) 15 flies/day
C) 14 flies/day
D) 17 flies/day
E) 16 flies/day
where t denotes the number of days since the beginning of the experiment. How fast was the population changing on the 20th day?
A) 18 flies/day
B) 15 flies/day
C) 14 flies/day
D) 17 flies/day
E) 16 flies/day
Question
The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by 
where t is measured in decades, with 
corresponding to the beginning of 1960.
Find the year when the percent of lay teachers was increasing most rapidly.
A) 1985
B) 1962
C) 1976
D) 1986
E) 1989
where t is measured in decades, with corresponding to the beginning of 1960. Find the year when the percent of lay teachers was increasing most rapidly.
A) 1985
B) 1962
C) 1976
D) 1986
E) 1989
Question
The U.S. population is approximated by the function 
, where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 (t = 3)? Round your answer to one decimal place.
__________ million
, where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 (t = 3)? Round your answer to one decimal place.
__________ million
Question
The percent of a certain brand of computer chips that will fail after t years of use is estimated to be 
.
What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place.
__________%
.
What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place.
__________%
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Question
Question
Question
Three hundred students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hours later is given by the function 
.
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours? __________
How fast was the news spreading 4 hours after the ceremony? Round the answer to the nearest integer. __________
.
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours? __________
How fast was the news spreading 4 hours after the ceremony? Round the answer to the nearest integer. __________
Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by 
.
How many children were stricken by the flu after the first day? Round your answer to the nearest integer.
__________ children
How many children had the flu after 10 days? Round your answer to the nearest integer.
__________ children
How many children eventually contracted the disease? Round your answer to the nearest integer.
__________ children
.
How many children were stricken by the flu after the first day? Round your answer to the nearest integer.
__________ children
How many children had the flu after 10 days? Round your answer to the nearest integer.
__________ children
How many children eventually contracted the disease? Round your answer to the nearest integer.
__________ children
Question
If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law 
, where p0 is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 17 lb/in.2 at sea level and 12.5 lb/in.2 at 6,000 ft, find the atmospheric pressure at an altitude of 18,000 ft. Please round the answer to one decimal place.
__________ lb/in.2
How fast is the atmospheric pressure changing with respect to altitude at an altitude of 18,000 ft? Please round the answer to four decimal places.
__________ lb/in.2/ft
, where p0 is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 17 lb/in.2 at sea level and 12.5 lb/in.2 at 6,000 ft, find the atmospheric pressure at an altitude of 18,000 ft. Please round the answer to one decimal place.
__________ lb/in.2
How fast is the atmospheric pressure changing with respect to altitude at an altitude of 18,000 ft? Please round the answer to four decimal places.
__________ lb/in.2/ft
Question
The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by 
where t measured in decades, with t = 0 corresponding to the beginning of 1960.
What percent of teachers were lay teachers at the beginning of 1990? Please round the answer to one decimal place.
__________ %
How fast was the percent of lay teachers changing at the beginning of 1990? Please round the answer to two decimal places.
__________ % / year
Find the year when the percent of lay teachers was increasing most rapidly.
where t measured in decades, with t = 0 corresponding to the beginning of 1960.
What percent of teachers were lay teachers at the beginning of 1990? Please round the answer to one decimal place.
__________ %
How fast was the percent of lay teachers changing at the beginning of 1990? Please round the answer to two decimal places.
__________ % / year
Find the year when the percent of lay teachers was increasing most rapidly.
Question
On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model 
, where t denotes the number of days since the beginning of the experiment.
What was the initial fruit fly population in the experiment? __________
What was the maximum fruit fly population that could be expected under this laboratory condition? __________
What was the population of the fruit fly colony on the 20th day? Please give the answer as an integer. __________
How fast was the population changing on the 20th day? Please give the answer as an integer. __________
, where t denotes the number of days since the beginning of the experiment.
What was the initial fruit fly population in the experiment? __________
What was the maximum fruit fly population that could be expected under this laboratory condition? __________
What was the population of the fruit fly colony on the 20th day? Please give the answer as an integer. __________
How fast was the population changing on the 20th day? Please give the answer as an integer. __________
Question
The length (in centimeters) of a typical Pacific halibut t years old is approximately 
. What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? Round your answers to the nearest tenth.
length of a typical halibut =
__________ cm
halibut increasing =
__________ cm/yr
maximum length =
__________ cm
. What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? Round your answers to the nearest tenth.length of a typical halibut =
__________ cm
halibut increasing =
__________ cm/yr
maximum length =
__________ cm
Question
Question
The radioactive element polonium decays according to the law 
, where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present?
__________ mg
, where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present?
__________ mg
Question
According to estimates by Paul Kroger Associates, the percent of households that own VCRs is given by 
, where t is measured in years, with t = 0 corresponding to the beginning of 1985.
What percent of households owned VCRs at the beginning of 1985? Round your answer to the nearest tenth.
__________%
At the beginning of 1992? Round your answer to the nearest tenth.
__________%
, where t is measured in years, with t = 0 corresponding to the beginning of 1985.
What percent of households owned VCRs at the beginning of 1985? Round your answer to the nearest tenth.
__________%
At the beginning of 1992? Round your answer to the nearest tenth.
__________%
Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Suppose a radioactive substance decays according to the formula 
. How long will it take for the substance to decay to half the original amount?
A) It will take 5,166 years for the substance to decay to half the original amount.
B) It will take 5,277 years for the substance to decay to half the original amount.
C) It will take 40 years for the substance to decay to half the original amount.
D) It will take 5,622 years for the substance to decay to half the original amount.
. How long will it take for the substance to decay to half the original amount? A) It will take 5,166 years for the substance to decay to half the original amount.
B) It will take 5,277 years for the substance to decay to half the original amount.
C) It will take 40 years for the substance to decay to half the original amount.
D) It will take 5,622 years for the substance to decay to half the original amount.
Question
The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by 
.
What is the rate of change of the strain with respect to the load when the load is 50 kg? When the load is 300 kg? Give the answers to four decimal places.
A) 0.0970
; 0.0240 
B) 0.1007
; 0.0240 
C) 0.0970
; 0.0216 
D) 0.1007
; 0.0216 
. What is the rate of change of the strain with respect to the load when the load is 50 kg? When the load is 300 kg? Give the answers to four decimal places.
A) 0.0970
; 0.0240 B) 0.1007
; 0.0240 C) 0.0970
; 0.0216 D) 0.1007
; 0.0216 Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find an equation of the tangent line to the graph of 
at the point 
.
A)
B)
C)
D)
at the point . A)
B)
C)
D)
Question
Use logarithmic differentiation to find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Use logarithmic differentiation to find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
For children between the ages of 5 and 13 years old, the Ehrenberg equation 
gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1.1 m to 1.3 m. Round the answer to the nearest tenth.
__________ kg
gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1.1 m to 1.3 m. Round the answer to the nearest tenth.
__________ kg
Question
Find the second derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
For children between the ages of 5 and 13 years old, the Ehrenberg equation 
gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1 m to 1.2 m.
A) 5.8 kg
B) 5.6 kg
C) 5.7 kg
D) 5.5 kg
E) 5.9 kg
gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1 m to 1.2 m. A) 5.8 kg
B) 5.6 kg
C) 5.7 kg
D) 5.5 kg
E) 5.9 kg
Question
Use the curve-sketching guideline, to select the graph of the function. 
A) 
B) 
C) 
A)
B)
C)
Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Use logarithmic differentiation to find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the second derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find the derivative of the function. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Find an equation of the tangent line to the graph of 
at its inflection point.
A)
B)
C)
D)
E)
at its inflection point. A)
B)
C)
D)
E)
Question
Find the inflection points of the function 
.
A)
B)
C)
D) There are no inflection points.
. A)
B)
C)
D) There are no inflection points.
Question
On the Richter scale, the magnitude R of an earthquake is given by the formula 
where I is the intensity of the earthquake being measured and I0 is the standard reference intensity. Suppose an earthquake is measured with a magnitude of 5 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Round your answer to the nearest integer.
A) 23,026I0
B) 23,086I0
C) 22,966I0
D) 22,906I0
E) 23,146I0
where I is the intensity of the earthquake being measured and I0 is the standard reference intensity. Suppose an earthquake is measured with a magnitude of 5 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Round your answer to the nearest integer. A) 23,026I0
B) 23,086I0
C) 22,966I0
D) 22,906I0
E) 23,146I0
Question
Find the derivative of the function.
Question
Find the derivative of the function.
Question
Find the derivative of the function.
Question
The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by 
.
Give the answer to four decimal places.
What is the rate of change of the strain with respect to the load when the load is 100 kg?
__________
What is the rate of change of the strain with respect to the load when the load is 350 kg?
__________
.
Give the answer to four decimal places.
What is the rate of change of the strain with respect to the load when the load is 100 kg?
__________
What is the rate of change of the strain with respect to the load when the load is 350 kg?
__________
Question
Find the derivative of the function.
Question
Use logarithmic differentiation to find the derivative of the function.
Question
Find the derivative of the function.
Question
Find the derivative of the function.
Question
Find the derivative of the function.
Question
Find the second derivative of the function.
Question
Find the derivative of the function.
Question
Find an equation of the tangent line to the graph of 
at the point 
.
at the point . Question
Find the second derivative of the function.
Question
Use logarithmic differentiation to find the derivative of the function.
Question
Find the derivative of the function.
Question
Find the inflection points of the function 
.
. Question
Find the derivative of the function.
Question
Find the derivative of the function.
Question
Find the derivative of the function.
Question
Use logarithmic differentiation to find the derivative of the function.
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Deck 5: Exponential and Logarithmic Functions
1
The concentration of a drug in grams/cubic centimeter (g/cm3) t minutes after it has been injected into the bloodstream is given by where w, p, and k are positive constants, with p > w.
At what time is the concentration of the drug the greatest? What will be the concentration of the drug in the long run?
A)
B)
C)
D)
where w, p, and k are positive constants, with p > w. At what time is the concentration of the drug the greatest? What will be the concentration of the drug in the long run?
A)
B)
C)
D)
2
The length (in centimeters) of a typical Pacific halibut t years old is approximately .
What is the length of a typical 5-year-old Pacific halibut? How fast is the length of a typical 5-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?
A) 85.8 cm; 14.5 cm/yr; 202 cm;
B) 115.6 cm; 13.8 cm/yr; 202 cm;
C) 128.7 cm; 0.952 cm/yr; 229 cm;
D) 202.0 cm; 11.7 cm/yr; 256 cm;
.
What is the length of a typical 5-year-old Pacific halibut? How fast is the length of a typical 5-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain?
A) 85.8 cm; 14.5 cm/yr; 202 cm;
B) 115.6 cm; 13.8 cm/yr; 202 cm;
C) 128.7 cm; 0.952 cm/yr; 229 cm;
D) 202.0 cm; 11.7 cm/yr; 256 cm;
115.6 cm; 13.8 cm/yr; 202 cm;
3
Skeletal remains of the so-called "Pittsburgh Man", unearthed in Pennsylvania, had lost 74% of the carbon 14 they originally contained. Determine the approximate age of the bones. Hint: the decay constant k for carbon 14 is equal to 0.00012.
A) The approximate age of bones is 10,103 year(s).
B) The approximate age of bones is 9,694 year(s).
C) The approximate age of bones is 7,770 year(s).
D) The approximate age of bones is 11,226 year(s).
A) The approximate age of bones is 10,103 year(s).
B) The approximate age of bones is 9,694 year(s).
C) The approximate age of bones is 7,770 year(s).
D) The approximate age of bones is 11,226 year(s).
The approximate age of bones is 11,226 year(s).
4
If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law where p0 is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 17 lb/in.2 at sea level and 11.5 lb/in.2 at 5,000 ft, how fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Give the answer to four decimal places.
A) 0.0004 lb/in.2/ft
B) 0.0006 lb/in.2/ft
C) 0.0003 lb/in.2/ft
D) 0.0007 lb/in.2/ft
E) 0.0005 lb/in.2/ft
where p0 is the atmospheric pressure at sea level and k is a constant. If the atmospheric pressure is 17 lb/in.2 at sea level and 11.5 lb/in.2 at 5,000 ft, how fast is the atmospheric pressure changing with respect to altitude at an altitude of 15,000 ft? Give the answer to four decimal places.
A) 0.0004 lb/in.2/ft
B) 0.0006 lb/in.2/ft
C) 0.0003 lb/in.2/ft
D) 0.0007 lb/in.2/ft
E) 0.0005 lb/in.2/ft
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5
A certain piece of machinery was purchased 2 year(s) ago by Garland Mills for $500,000. Its present resale value is $320,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 year(s) from now?
A) The resale value of the machinery will be $204,800
B) The resale value of the machinery will be $205,911
C) The resale value of the machinery will be $204,789
D) The resale value of the machinery will be $204,911
A) The resale value of the machinery will be $204,800
B) The resale value of the machinery will be $205,911
C) The resale value of the machinery will be $204,789
D) The resale value of the machinery will be $204,911
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6
The percent of a certain brand of computer chips that will fail after t years of use is estimated to be .
What percent of this brand of computer chips are expected to be usable after 6 years?
A) 71.3%
B) 56.7%
C) 69.9%
D) 64.2%
.
What percent of this brand of computer chips are expected to be usable after 6 years?
A) 71.3%
B) 56.7%
C) 69.9%
D) 64.2%
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7
Three hundred students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hours later is given by the function .
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours?
A) 1,100
B) 1,085
C) 1,095
D) 1,090
E) 1,080
. If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours?
A) 1,100
B) 1,085
C) 1,095
D) 1,090
E) 1,080
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8
Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by .
Select the graph of this function. At what level is the demand expected to stabilize?
A) 1,900 computers
B) 1,800 computers
C) 2,100 computers
D) 1,800 computers
E) 1,900 computers
. Select the graph of this function. At what level is the demand expected to stabilize?
A)
1,900 computersB)
1,800 computers C)
2,100 computers D)
1,800 computers E)
1,900 computers Unlock Deck
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9
Given that a quantity Q(t) exhibiting exponential decay is described by the function where t is measured in years. What is the decay constant? What quantity is present initially? Complete the table of values. Round your answer to the nearest integer.
A)
B)
C)
D)
where t is measured in years. What is the decay constant? What quantity is present initially? Complete the table of values. Round your answer to the nearest integer.A)
B)
C)
D)
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10
Phosphorus 32 has a half-life of 14.2 days. If 600 g of this substance are present initially, find the amount present after t days. What amount will be left after 3.55 days? How fast is the phosphorus 32 decaying when t = 3.55?
A)
B)
C)
D)
A)
B)
C)
D)
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11
Given that a quantity Q(t) is described by the exponential growth function where t is measured in minutes. What is the growth constant? What quantity is present initially? Complete the table of values. Round your answers to the nearest integer. t
A)
B)
C)
D)
where t is measured in minutes. What is the growth constant? What quantity is present initially? Complete the table of values. Round your answers to the nearest integer. tA)
B)
C)
D)
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12
The U.S. population is approximated by the function where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 ( t = 3 )?
A) 408.0 millions
B) 322.6 millions
C) 616.3 millions
D) 325.6 millions
where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 ( t = 3 )? A) 408.0 millions
B) 322.6 millions
C) 616.3 millions
D) 325.6 millions
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13
The radioactive element polonium decays according to the law where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present?
A) The initial amount was 645 mg
B) The initial amount was 642 mg
C) The initial amount was 651 mg
D) The initial amount was 640 mg
where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present? A) The initial amount was 645 mg
B) The initial amount was 642 mg
C) The initial amount was 651 mg
D) The initial amount was 640 mg
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14
The growth rate of the bacterium, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 20 min. If the initial cell population is 10, determine the function Q(t) that expresses the exponential growth of the number of cells of this bacterium as a function of time t (in minutes). How long will it take for a colony of 10 cells to increase to a population of 1 million? If the initial cell population were 100, how would this alter the model?
A)
B)
C)
D)
A)
B)
C)
D)
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15
During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by .
How many children were stricken by the flu after the first day? How many children had the flu after 10 days? How many children eventually contracted the disease?
A) 12 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,400 children eventually contracted the disease
B) 15 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,083 children eventually contracted the disease
C) 17 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,246 children eventually contracted the disease
D) 15 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,400 children eventually contracted the disease
. How many children were stricken by the flu after the first day? How many children had the flu after 10 days? How many children eventually contracted the disease?
A) 12 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,400 children eventually contracted the disease
B) 15 children were stricken by the flu after the first day; 1,451 children had the flu after 10 days; 1,083 children eventually contracted the disease
C) 17 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,246 children eventually contracted the disease
D) 15 children were stricken by the flu after the first day; 1,312 children had the flu after 10 days; 1,400 children eventually contracted the disease
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16
According to estimates by Paul Kroger Associates, the percent of households that own VCRs is given by where t is measured in years, with t = 0 corresponding to the beginning of 1985. What percent of households owned VCRs at the beginning of 1985? At the beginning of 1990?
A) 5.0%; 33.6%
B) 5.0%; 34.3%
C) 34.3%; 65.0%
D) 2.9%; 32.9%
where t is measured in years, with t = 0 corresponding to the beginning of 1985. What percent of households owned VCRs at the beginning of 1985? At the beginning of 1990? A) 5.0%; 33.6%
B) 5.0%; 34.3%
C) 34.3%; 65.0%
D) 2.9%; 32.9%
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17
Wood deposits recovered from an archeological site contain 24% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.
A) The tree died 11,893 year(s) ago.
B) The tree died 13,425 year(s) ago.
C) The tree died 8,437 year(s) ago.
D) The tree died 10,770 year(s) ago.
A) The tree died 11,893 year(s) ago.
B) The tree died 13,425 year(s) ago.
C) The tree died 8,437 year(s) ago.
D) The tree died 10,770 year(s) ago.
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18
Strontium 90, a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. If the amount of strontium 90 in a certain area is found to be eight times the "safe" level, find how much time must elapse before an "acceptable level" is reached.
A) 81 year(s) must elapse before an "acceptable level" is reached.
B) 78 year(s) must elapse before an "acceptable level" is reached.
C) 66 year(s) must elapse before an "acceptable level" is reached.
D) 57.3 year(s) must elapse before an "acceptable level" is reached.
A) 81 year(s) must elapse before an "acceptable level" is reached.
B) 78 year(s) must elapse before an "acceptable level" is reached.
C) 66 year(s) must elapse before an "acceptable level" is reached.
D) 57.3 year(s) must elapse before an "acceptable level" is reached.
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19
On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model where t denotes the number of days since the beginning of the experiment.
How fast was the population changing on the 20th day?
A) 18 flies/day
B) 15 flies/day
C) 14 flies/day
D) 17 flies/day
E) 16 flies/day
where t denotes the number of days since the beginning of the experiment. How fast was the population changing on the 20th day?
A) 18 flies/day
B) 15 flies/day
C) 14 flies/day
D) 17 flies/day
E) 16 flies/day
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20
The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by where t is measured in decades, with corresponding to the beginning of 1960.
Find the year when the percent of lay teachers was increasing most rapidly.
A) 1985
B) 1962
C) 1976
D) 1986
E) 1989
where t is measured in decades, with corresponding to the beginning of 1960. Find the year when the percent of lay teachers was increasing most rapidly.
A) 1985
B) 1962
C) 1976
D) 1986
E) 1989
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21
The U.S. population is approximated by the function , where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 (t = 3)? Round your answer to one decimal place.
__________ million
, where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 (t = 3)? Round your answer to one decimal place.
__________ million
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22
The percent of a certain brand of computer chips that will fail after t years of use is estimated to be .
What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place.
__________%
.
What percent of this brand of computer chips are expected to be usable after 6 years? Round your answer to one decimal place.
__________%
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23
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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25
Strontium 90, a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. If the amount of strontium 90 in a certain area is found to be eight times the "safe" level, find how much time must elapse before an "acceptable level" is reached.
__________ years
__________ years
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26
Skeletal remains of the so-called "Pittsburgh Man", unearthed in Pennsylvania, had lost 74% of the carbon 14 they originally contained. Determine the approximate age of the bones. Round your answer to the nearest year.
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27
Wood deposits recovered from an archeological site contain 28% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Round your answer to the nearest year.
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28
Three hundred students attended the dedication ceremony of a new building on a college campus. The president of the traditionally female college announced a new expansion program, which included plans to make the college coeducational. The number of students who learned of the new program t hours later is given by the function .
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours? __________
How fast was the news spreading 4 hours after the ceremony? Round the answer to the nearest integer. __________
.
If 600 students on campus had heard about the new program 2 hours after the ceremony, how many students had heard about the policy after 4 hours? __________
How fast was the news spreading 4 hours after the ceremony? Round the answer to the nearest integer. __________
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29
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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30
During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by .
How many children were stricken by the flu after the first day? Round your answer to the nearest integer.
__________ children
How many children had the flu after 10 days? Round your answer to the nearest integer.
__________ children
How many children eventually contracted the disease? Round your answer to the nearest integer.
__________ children
.
How many children were stricken by the flu after the first day? Round your answer to the nearest integer.
__________ children
How many children had the flu after 10 days? Round your answer to the nearest integer.
__________ children
How many children eventually contracted the disease? Round your answer to the nearest integer.
__________ children
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31
If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law , where p0 is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 17 lb/in.2 at sea level and 12.5 lb/in.2 at 6,000 ft, find the atmospheric pressure at an altitude of 18,000 ft. Please round the answer to one decimal place.
__________ lb/in.2
How fast is the atmospheric pressure changing with respect to altitude at an altitude of 18,000 ft? Please round the answer to four decimal places.
__________ lb/in.2/ft
, where p0 is the atmospheric pressure at sea level and k is a constant.
If the atmospheric pressure is 17 lb/in.2 at sea level and 12.5 lb/in.2 at 6,000 ft, find the atmospheric pressure at an altitude of 18,000 ft. Please round the answer to one decimal place.
__________ lb/in.2
How fast is the atmospheric pressure changing with respect to altitude at an altitude of 18,000 ft? Please round the answer to four decimal places.
__________ lb/in.2/ft
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32
The change from religious to lay teachers at Roman Catholic schools has been partly attributed to the decline in the number of women and men entering religious orders. The percent of teachers who are lay teachers is given by where t measured in decades, with t = 0 corresponding to the beginning of 1960.
What percent of teachers were lay teachers at the beginning of 1990? Please round the answer to one decimal place.
__________ %
How fast was the percent of lay teachers changing at the beginning of 1990? Please round the answer to two decimal places.
__________ % / year
Find the year when the percent of lay teachers was increasing most rapidly.
where t measured in decades, with t = 0 corresponding to the beginning of 1960.
What percent of teachers were lay teachers at the beginning of 1990? Please round the answer to one decimal place.
__________ %
How fast was the percent of lay teachers changing at the beginning of 1990? Please round the answer to two decimal places.
__________ % / year
Find the year when the percent of lay teachers was increasing most rapidly.
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33
On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model , where t denotes the number of days since the beginning of the experiment.
What was the initial fruit fly population in the experiment? __________
What was the maximum fruit fly population that could be expected under this laboratory condition? __________
What was the population of the fruit fly colony on the 20th day? Please give the answer as an integer. __________
How fast was the population changing on the 20th day? Please give the answer as an integer. __________
, where t denotes the number of days since the beginning of the experiment.
What was the initial fruit fly population in the experiment? __________
What was the maximum fruit fly population that could be expected under this laboratory condition? __________
What was the population of the fruit fly colony on the 20th day? Please give the answer as an integer. __________
How fast was the population changing on the 20th day? Please give the answer as an integer. __________
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34
The length (in centimeters) of a typical Pacific halibut t years old is approximately . What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? Round your answers to the nearest tenth.
length of a typical halibut =
__________ cm
halibut increasing =
__________ cm/yr
maximum length =
__________ cm
. What is the length of a typical 6-year-old Pacific halibut? How fast is the length of a typical 6-year-old Pacific halibut increasing? What is the maximum length a typical Pacific halibut can attain? Round your answers to the nearest tenth.length of a typical halibut =
__________ cm
halibut increasing =
__________ cm/yr
maximum length =
__________ cm
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35
A certain piece of machinery was purchased 5 years ago by Garland Mills for $400,000. Its present resale value is $256,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 years from now? Round your answer to the nearest dollar.
$__________
$__________
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36
The radioactive element polonium decays according to the law , where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present?
__________ mg
, where Q0 is the initial amount and the time t is measured in days. If the amount of polonium left after 280 days is 80 mg, what was the initial amount present?
__________ mg
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37
According to estimates by Paul Kroger Associates, the percent of households that own VCRs is given by , where t is measured in years, with t = 0 corresponding to the beginning of 1985.
What percent of households owned VCRs at the beginning of 1985? Round your answer to the nearest tenth.
__________%
At the beginning of 1992? Round your answer to the nearest tenth.
__________%
, where t is measured in years, with t = 0 corresponding to the beginning of 1985.
What percent of households owned VCRs at the beginning of 1985? Round your answer to the nearest tenth.
__________%
At the beginning of 1992? Round your answer to the nearest tenth.
__________%
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38
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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39
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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40
Suppose a radioactive substance decays according to the formula . How long will it take for the substance to decay to half the original amount?
A) It will take 5,166 years for the substance to decay to half the original amount.
B) It will take 5,277 years for the substance to decay to half the original amount.
C) It will take 40 years for the substance to decay to half the original amount.
D) It will take 5,622 years for the substance to decay to half the original amount.
. How long will it take for the substance to decay to half the original amount? A) It will take 5,166 years for the substance to decay to half the original amount.
B) It will take 5,277 years for the substance to decay to half the original amount.
C) It will take 40 years for the substance to decay to half the original amount.
D) It will take 5,622 years for the substance to decay to half the original amount.
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41
The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by .
What is the rate of change of the strain with respect to the load when the load is 50 kg? When the load is 300 kg? Give the answers to four decimal places.
A) 0.0970 ; 0.0240
B) 0.1007 ; 0.0240
C) 0.0970 ; 0.0216
D) 0.1007 ; 0.0216
. What is the rate of change of the strain with respect to the load when the load is 50 kg? When the load is 300 kg? Give the answers to four decimal places.
A) 0.0970
; 0.0240 B) 0.1007
; 0.0240 C) 0.0970
; 0.0216 D) 0.1007
; 0.0216 Unlock Deck
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42
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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43
Find an equation of the tangent line to the graph of at the point .
A)
B)
C)
D)
at the point . A)
B)
C)
D)
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44
Use logarithmic differentiation to find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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45
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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46
Use logarithmic differentiation to find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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47
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
For children between the ages of 5 and 13 years old, the Ehrenberg equation gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1.1 m to 1.3 m. Round the answer to the nearest tenth.
__________ kg
gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1.1 m to 1.3 m. Round the answer to the nearest tenth.
__________ kg
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49
Find the second derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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50
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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51
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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52
For children between the ages of 5 and 13 years old, the Ehrenberg equation gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1 m to 1.2 m.
A) 5.8 kg
B) 5.6 kg
C) 5.7 kg
D) 5.5 kg
E) 5.9 kg
gives the relationship between the weight W (in kilograms) and the height h (in meters) of a child. Use differentials to estimate the change in the weight of a child who grows from 1 m to 1.2 m. A) 5.8 kg
B) 5.6 kg
C) 5.7 kg
D) 5.5 kg
E) 5.9 kg
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53
Use the curve-sketching guideline, to select the graph of the function.
A)
B)
C)
A)
B)
C)
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54
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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55
Use logarithmic differentiation to find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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56
Find the second derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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57
Find the derivative of the function.
A)
B)
C)
D)
A)
B)
C)
D)
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58
Find an equation of the tangent line to the graph of at its inflection point.
A)
B)
C)
D)
E)
at its inflection point. A)
B)
C)
D)
E)
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59
Find the inflection points of the function .
A)
B)
C)
D) There are no inflection points.
. A)
B)
C)
D) There are no inflection points.
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60
On the Richter scale, the magnitude R of an earthquake is given by the formula where I is the intensity of the earthquake being measured and I0 is the standard reference intensity. Suppose an earthquake is measured with a magnitude of 5 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Round your answer to the nearest integer.
A) 23,026I0
B) 23,086I0
C) 22,966I0
D) 22,906I0
E) 23,146I0
where I is the intensity of the earthquake being measured and I0 is the standard reference intensity. Suppose an earthquake is measured with a magnitude of 5 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake. Round your answer to the nearest integer. A) 23,026I0
B) 23,086I0
C) 22,966I0
D) 22,906I0
E) 23,146I0
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61
Find the derivative of the function.
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62
Find the derivative of the function.
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63
Find the derivative of the function.
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64
The strain (percent of compression) on the lumbar vertebral disks in an adult human as a function of the load x (in kilograms) is given by .
Give the answer to four decimal places.
What is the rate of change of the strain with respect to the load when the load is 100 kg?
__________
What is the rate of change of the strain with respect to the load when the load is 350 kg?
__________
.
Give the answer to four decimal places.
What is the rate of change of the strain with respect to the load when the load is 100 kg?
__________
What is the rate of change of the strain with respect to the load when the load is 350 kg?
__________
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65
Find the derivative of the function.
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66
Use logarithmic differentiation to find the derivative of the function.
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67
Find the derivative of the function.
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68
Find the derivative of the function.
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69
Find the derivative of the function.
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70
Find the second derivative of the function.
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71
Find the derivative of the function.
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72
Find an equation of the tangent line to the graph of at the point .
at the point . Unlock Deck
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73
Find the second derivative of the function.
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74
Use logarithmic differentiation to find the derivative of the function.
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75
Find the derivative of the function.
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76
Find the inflection points of the function .
. Unlock Deck
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77
Find the derivative of the function.
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78
Find the derivative of the function.
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79
Find the derivative of the function.
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80
Use logarithmic differentiation to find the derivative of the function.
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