تكلم مع الذكاء الاصطناعي
Deck 4: Exponential and Logarithmic Functions
ملء الشاشة (f)
سؤال
Determine which of the following functions is graphed below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the exponential function below for 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
Evaluate the exponential function 
for 
.
A)
B)
C)
D)
E)
for .A)
B)
C)
D)
E)
سؤال
Determine which of the following functions is graphed below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Explain how to use the graph of 
to produce the graph of 
.
A)Shift the graph of f horizontally 2 units to the right and then shift this graph vertically downward 8 units.
B)Shift the graph of f horizontally 8 units to the right and then shift this graph vertically upward 2 units.
C)Shift the graph of f horizontally 2 units to the right and then shift this graph vertically upward 8 units.
D)Shift the graph of f horizontally 8 units to the left and then shift this graph vertically downward 2 units.
E)Shift the graph of f horizontally 2 units to the left and then shift this graph vertically downward 8 units.
to produce the graph of .A)Shift the graph of f horizontally 2 units to the right and then shift this graph vertically downward 8 units.
B)Shift the graph of f horizontally 8 units to the right and then shift this graph vertically upward 2 units.
C)Shift the graph of f horizontally 2 units to the right and then shift this graph vertically upward 8 units.
D)Shift the graph of f horizontally 8 units to the left and then shift this graph vertically downward 2 units.
E)Shift the graph of f horizontally 2 units to the left and then shift this graph vertically downward 8 units.
سؤال
Sketch the graph of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
The monthly earnings in dollars, of a software sales executive is given by 
where s is the value, in dollars, of the software sold by the executive during the month. Find 
A)
B)
C)
D)
E)
where s is the value, in dollars, of the software sold by the executive during the month. Find A)
B)
C)
D)
E)
سؤال
If 
is in the domain of 
, find 
A)
B)
C)
D)
E)
is in the domain of , find A)
B)
C)
D)
E)
سؤال
Find the inverse of 
, 
.
A)
B)
C)
D)
E)
, .A)
B)
C)
D)
E)
سؤال
Assuming that 
has an inverse function, if 
find 
.
A)
B)
C)
D)
E)
has an inverse function, if find .A)
B)
C)
D)
E)
سؤال
If f is a one-to-one function and 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use composition of functions to determine whether 
and 
are inverses of one another.
and are inverses of one another. سؤال
Find the inverse of the function below, if one exists. 
A)
B)
C)
D)no inverse exists
E)
A)
B)
C)
D)no inverse exists
E)
سؤال
Use composition of functions to determine whether 
and 
are inverses of one another.
and are inverses of one another. سؤال
Draw the graph of the inverse relation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Draw the graph of the inverse relation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The function 
converts a men s shoe size in the United States to the equivalent shoe size in another country. Determine the function 
that can be used to convert the other country s shoe size to its equivalent U.S. shoe size.
A)
B)
C)
D)
E)
converts a men s shoe size in the United States to the equivalent shoe size in another country. Determine the function that can be used to convert the other country s shoe size to its equivalent U.S. shoe size.A)
B)
C)
D)
E)
سؤال
Explain how to use the graph of 
to produce the graph of 
.
A)Reflect the graph of f across the x-axis.
B)Reflect the graph of f across the x- and y-axes.
C)Shift the graph of f horizontally to the right 1 unit.
D)Shift the graph of f vertically downward 1 unit.
E)Reflect the graph of f across the y-axis.
to produce the graph of .A)Reflect the graph of f across the x-axis.
B)Reflect the graph of f across the x- and y-axes.
C)Shift the graph of f horizontally to the right 1 unit.
D)Shift the graph of f vertically downward 1 unit.
E)Reflect the graph of f across the y-axis.
سؤال
For 
, find 
. State any restrictions on the domain of 
.
A)
B)
C)
D)
E)
, find . State any restrictions on the domain of .A)
B)
C)
D)
E)
سؤال
Find 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
Write the exponential equation 
in its logarithmic form.
A)
B)
C)
D)
E)
in its logarithmic form.A)
B)
C)
D)
E)
سؤال
Find the domain of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Sketch the graph of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
The demand d for a specific product, in items per month, is given by 
where p is the price, in dollars, of the product. What will happen to the demand as the price increases without bound?
A)The demand will approach 0 items per month.
B)The demand will approach
items per month.
C)The demand will approach
items per month.
D)The demand will approach
items per month.
E)The demand will increase without bound.
where p is the price, in dollars, of the product. What will happen to the demand as the price increases without bound?A)The demand will approach 0 items per month.
B)The demand will approach
items per month.C)The demand will approach
items per month.D)The demand will approach
items per month.E)The demand will increase without bound.
سؤال
Find the domain of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Graph the function below by using its exponential form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write the equation below in its exponential form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write the equation below in its logarithmic form. Assume 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
The function 
gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Use a graphing utility to determine how long it will take, to the nearest minute, for the amount of medication in the patient s bloodstream to reach 175 milligrams.
A)14 min
B)2 min
C)21 min
D)39 min
E)9 min
gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Use a graphing utility to determine how long it will take, to the nearest minute, for the amount of medication in the patient s bloodstream to reach 175 milligrams.A)14 min
B)2 min
C)21 min
D)39 min
E)9 min
سؤال
Evaluate the logarithm 
without using a calculator.
A)
B)2
C)16
D)
E)3
without using a calculator.A)
B)2
C)16
D)
E)3
سؤال
Shielding is used to contain radiation. The percentage of a certain radiation that can penetrate x millimeters of shielding is given by 
How many millimeters of shielding are required so that less than 
% of the radiation penetrates the shielding? Round to the nearest millimeter.
A)25 millimeters
B)8 millimeters
C)6 millimeters
D)10 millimeters
E)28 millimeters
How many millimeters of shielding are required so that less than % of the radiation penetrates the shielding? Round to the nearest millimeter.A)25 millimeters
B)8 millimeters
C)6 millimeters
D)10 millimeters
E)28 millimeters
سؤال
Find the domain of the function. Write the domain using interval notation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Shielding is used to contain radiation. The percentage of a certain radiation that can penetrate x millimeters of shielding is given by 
What percentage of radiation, to the nearest tenth of a percent, will penetrate a shield that is 
millimeters thick?
A)
%
B)
%
C)
%
D)
%
E)
%
What percentage of radiation, to the nearest tenth of a percent, will penetrate a shield that is millimeters thick?A)
%B)
%C)
%D)
%E)
% سؤال
The function 
gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Find the amount of medication, to the nearest milligram, in the patient s bloodstream after 15 minutes.
A)231 mg
B)182 mg
C)249 mg
D)4 mg
E)15 mg
gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Find the amount of medication, to the nearest milligram, in the patient s bloodstream after 15 minutes.A)231 mg
B)182 mg
C)249 mg
D)4 mg
E)15 mg
سؤال
Write the logarithmic equation 
in its exponential form.
A)
B)
C)
D)
E)
in its exponential form.A)
B)
C)
D)
E)
سؤال
Evaluate the logarithm below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A cup of coffee is heated to 
F and placed in a room that maintains a temperature of 
F. The temperature of the coffee after t minutes is given by 
. Use a graphing utility to determine when, to the nearest tenth of a minute, the temperature of the coffee will reach 
F.
A)26.8 min
B)2.9 min
C)
min
D)13.6 min
E)42.3 min
F and placed in a room that maintains a temperature of F. The temperature of the coffee after t minutes is given by . Use a graphing utility to determine when, to the nearest tenth of a minute, the temperature of the coffee will reach F.A)26.8 min
B)2.9 min
C)
minD)13.6 min
E)42.3 min
سؤال
A cup of coffee is heated to 160 F and placed in a room that maintains a temperature of 60 F. The temperature of the coffee after t minutes is given by 
. Find the temperature, to the nearest degree, of the coffee 45 minutes after it is placed in the room.
A)82° F
B)123° F
C)115° F
D)35° F
E)56° F
. Find the temperature, to the nearest degree, of the coffee 45 minutes after it is placed in the room.A)82° F
B)123° F
C)115° F
D)35° F
E)56° F
سؤال
Evaluate the logarithm 
without using a calculator.
A)3
B)-3
C)-2
D)2
E)100
without using a calculator.A)3
B)-3
C)-2
D)2
E)100
سؤال
The demand d for a specific product, in items per month, is given by 
where p is the price, in dollars, of the product. What will be the monthly demand, to the nearest unit, when the price of the product is $ 
.
A)
units
B)
units
C)
units
D)
units
E)
units
where p is the price, in dollars, of the product. What will be the monthly demand, to the nearest unit, when the price of the product is $ .A)
unitsB)
unitsC)
unitsD)
unitsE)
units سؤال
Use algebraic procedures to find the exact solution of the equation 
.
A)3
B)1
C)243
D)7
E)729
.A)3
B)1
C)243
D)7
E)729
سؤال
Expand the logarithmic expression 
Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
سؤال
Write the expression below as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The function 
models the relationship between the dollar amount x spent on advertising a product and the number of units N that a company can sell. Find the number of units that will be sold with advertising expenditures of $ 
.
A)
units
B)
units
C)
units
D)
units
E)
units
models the relationship between the dollar amount x spent on advertising a product and the number of units N that a company can sell. Find the number of units that will be sold with advertising expenditures of $ .A)
unitsB)
unitsC)
unitsD)
unitsE)
units سؤال
The function 
models the average typing speed S , in words per minute, of a student who has been typing for t months. What was the student s average typing speed, to the nearest word per minute, after 10 months?
A)29 words/min
B)64 words/min
C)28 words/min
D)29 words/min.
E)67 words/min
models the average typing speed S , in words per minute, of a student who has been typing for t months. What was the student s average typing speed, to the nearest word per minute, after 10 months?A)29 words/min
B)64 words/min
C)28 words/min
D)29 words/min.
E)67 words/min
سؤال
Use algebraic procedures to find the exact solution(s)of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
An earthquake in South America had an intensity of 
. What did it measure on the Richter scale?
A)1.3
B)7.7
C)2.0
D)17.7
E)5.0
. What did it measure on the Richter scale?A)1.3
B)7.7
C)2.0
D)17.7
E)5.0
سؤال
A rainstorm in New York City produced rainwater with a pH of 8.1. Determine the hydronium-ion concentration of the rainwater.
A)
mol/L
B)
mol/L
C)
mol/L
D)
mol/L
E)
mol/L
A)
mol/LB)
mol/LC)
mol/LD)
mol/LE)
mol/L سؤال
A chemical solution has a hydronium-ion concentration of 
mole per liter. Determine the pH of the solution.
A)10.7
B)8.8
C)21.5
D)9.3
E)4.6
mole per liter. Determine the pH of the solution.A)10.7
B)8.8
C)21.5
D)9.3
E)4.6
سؤال
The number of digits N in the expansion of 
, where both b and x are positive integers, is 
where 
denotes the nearest integer less than or equal to 
Find the number of digits in 
.
A)
digits
B)
digits
C)
digits
D)
digits
E)
digits
, where both b and x are positive integers, is where denotes the nearest integer less than or equal to Find the number of digits in .A)
digitsB)
digitsC)
digitsD)
digitsE)
digits سؤال
سؤال
The function 
gives the annual interest rate r , as a percent, that a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What interest rate, to the nearest tenth of a percent, will the bank pay on a money market account with a term of 5 months?
A)1.58%
B)2.55%
C)2.06%
D)1.29%
E)
%
gives the annual interest rate r , as a percent, that a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What interest rate, to the nearest tenth of a percent, will the bank pay on a money market account with a term of 5 months?A)1.58%
B)2.55%
C)2.06%
D)1.29%
E)
% سؤال
The function 
models the average typing speed S , in words per minute, of a student who has been typing for t months. Use a graph of S to determine how long, to the nearest tenth of a month, it will take the student to achieve an average typing speed of 68 words per minute.
A)5.6 months
B)7.5 months
C)1.8 months
D)5.2 months
E)1.9 months
models the average typing speed S , in words per minute, of a student who has been typing for t months. Use a graph of S to determine how long, to the nearest tenth of a month, it will take the student to achieve an average typing speed of 68 words per minute.A)5.6 months
B)7.5 months
C)1.8 months
D)5.2 months
E)1.9 months
سؤال
The function 
gives the annual interest rate r , as a percent, a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What is the minimum number of complete months during which a person must invest to receive an interest rate of at least 2.3%?
A)17 months
B)10 months
C)19 months
D)16 months
E)8 months
gives the annual interest rate r , as a percent, a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What is the minimum number of complete months during which a person must invest to receive an interest rate of at least 2.3%?A)17 months
B)10 months
C)19 months
D)16 months
E)8 months
سؤال
Evaluate the following logarithmic expression. 
A)6
B)9
C)5
D)4
E)1
A)6
B)9
C)5
D)4
E)1
سؤال
Use the change-of-base formula to graph the logarithmic function below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Expand the given logarithmic expression. Assume all variable expressions represent positive real numbers. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write 
as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
سؤال
Use the change-of-base formula to approximate the logarithm below. Round your answer to four decimal places. 
A)-0.3365
B)-0.4854
C)-0.1682
D)0.8271
E)0.6099
A)-0.3365
B)-0.4854
C)-0.1682
D)0.8271
E)0.6099
سؤال
An earthquake that occurred on the West Coast of the United States had a Richter scale magnitude of 7.6. Find the intensity of this earthquake.
A)39,810,717
B)642,888,893
C)9
D)1998
E)76
A)39,810,717
B)642,888,893
C)9
D)1998
E)76
سؤال
سؤال
A model for how long our coal resources will last is given by 
where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. If our consumption of coal increases by 14% per year, in how many years will we deplete our coal resources?
A)88 years
B)14 years
C)29 years
D)67 years
E)39 years
where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. If our consumption of coal increases by 14% per year, in how many years will we deplete our coal resources?A)88 years
B)14 years
C)29 years
D)67 years
E)39 years
سؤال
If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by 
. Determine the velocity, to the nearest hundredth of a foot per second, of the object after 1.9 seconds.
A)0.07 ft/sec
B)13.75 ft/sec
C)0.16 ft/sec
D)16.93 ft/sec
E)14.84 ft/sec
. Determine the velocity, to the nearest hundredth of a foot per second, of the object after 1.9 seconds.A)0.07 ft/sec
B)13.75 ft/sec
C)0.16 ft/sec
D)16.93 ft/sec
E)14.84 ft/sec
سؤال
Use algebraic procedures to find the exact solution of the equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use algebraic procedures to find the exact solution of the equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use algebraic procedures to find the exact solution of the equation 
.
A)-1, 13
B)
C)
D)1
E)
.A)-1, 13
B)
C)
D)1
E)
سؤال
Use algebraic procedures to find the exact solution of the equation 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
An industrial psychologist has determined that the average percent score for an employee on a test of the employee s knowledge of the company s product is given by 
where t is the number of weeks on the job and P is the percent score. Determine the horizontal asymptote of the graph of P .
A)
B)
C)
D)
E)
where t is the number of weeks on the job and P is the percent score. Determine the horizontal asymptote of the graph of P .A)
B)
C)
D)
E)
سؤال
Use algebraic procedures to find the exact solution(s)of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use algebraic procedures to find the exact solution of the equation 
.
A)
B)0, -8
C)9
D)
E)1
.A)
B)0, -8
C)9
D)
E)1
سؤال
The population P of a city grows exponentially according to the function 
where t is measured in years. Find the population at time 
.
A)32,364 people
B)21,280 people
C)10,580 people
D)16,091 people
E)9200 people
where t is measured in years. Find the population at time .A)32,364 people
B)21,280 people
C)10,580 people
D)16,091 people
E)9200 people
سؤال
The population P of a city grows exponentially according to the function 
where t is measured in years. When, to the nearest year, will the population reach 15,000?
A)in 5.5 years
B)in 8 years
C)in 3 years
D)in 12 years
E)in 10 years
where t is measured in years. When, to the nearest year, will the population reach 15,000?A)in 5.5 years
B)in 8 years
C)in 3 years
D)in 12 years
E)in 10 years
سؤال
Use algebraic procedures to find the exact solution(s)of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the decay function for the amount of radioactive material that remains in a sample after t days if the half-life of the material is 29 days.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The population of a mid-sized city is growing exponentially. The population of the city was 250,000 in the year 2000 and 273,400 in 2004. Find the exponential growth function that models the population growth of the city. Use 
to represent the year 2000.
A)
B)
C)
D)
E)
to represent the year 2000.A)
B)
C)
D)
E)
سؤال
If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by 
. Determine the vertical asymptote for the graph of this function.
A)
B)
C)
D)
E)
. Determine the vertical asymptote for the graph of this function.A)
B)
C)
D)
E)
سؤال
Use algebraic procedures to find the exact solution of the equation 
.
A)
B)
C)
D)
E)no solution
.A)
B)
C)
D)
E)no solution
سؤال
A model for how long our coal resources will last is given by 
where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. What percent increase in consumption of coal will deplete the resources in 38.1 years? Round to the nearest tenth of a percent.
A)9.9%
B)8.7%
C)10.5%
D)10.1%
E)8.1%
where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. What percent increase in consumption of coal will deplete the resources in 38.1 years? Round to the nearest tenth of a percent.A)9.9%
B)8.7%
C)10.5%
D)10.1%
E)8.1%
سؤال
An industrial psychologist has determined that the average percent score for an employee on a test of the employee s knowledge of the company s product is given by 
where t is the number of weeks on the job and P is the percent score. Estimate (to the nearest week)the expected number of weeks of employment that are necessary for an employee to earn a 95% score on the test.
A)35 weeks
B)21 weeks
C)55 weeks
D)6 weeks
E)68 weeks
where t is the number of weeks on the job and P is the percent score. Estimate (to the nearest week)the expected number of weeks of employment that are necessary for an employee to earn a 95% score on the test.A)35 weeks
B)21 weeks
C)55 weeks
D)6 weeks
E)68 weeks
سؤال
The number of bacteria present in a culture at time t hours is given by 
. Find the number of bacteria present when 
.
A)47,500
B)29,687,500
C)237,500
D)9500
E)5,937,500
. Find the number of bacteria present when .A)47,500
B)29,687,500
C)237,500
D)9500
E)5,937,500
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العب
ملء الشاشة (f)
Deck 4: Exponential and Logarithmic Functions
1
Determine which of the following functions is graphed below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Evaluate the exponential function below for .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
3
Evaluate the exponential function for .
A)
B)
C)
D)
E)
for .A)
B)
C)
D)
E)
4
Determine which of the following functions is graphed below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Explain how to use the graph of to produce the graph of .
A)Shift the graph of f horizontally 2 units to the right and then shift this graph vertically downward 8 units.
B)Shift the graph of f horizontally 8 units to the right and then shift this graph vertically upward 2 units.
C)Shift the graph of f horizontally 2 units to the right and then shift this graph vertically upward 8 units.
D)Shift the graph of f horizontally 8 units to the left and then shift this graph vertically downward 2 units.
E)Shift the graph of f horizontally 2 units to the left and then shift this graph vertically downward 8 units.
to produce the graph of .A)Shift the graph of f horizontally 2 units to the right and then shift this graph vertically downward 8 units.
B)Shift the graph of f horizontally 8 units to the right and then shift this graph vertically upward 2 units.
C)Shift the graph of f horizontally 2 units to the right and then shift this graph vertically upward 8 units.
D)Shift the graph of f horizontally 8 units to the left and then shift this graph vertically downward 2 units.
E)Shift the graph of f horizontally 2 units to the left and then shift this graph vertically downward 8 units.
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6
Sketch the graph of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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7
The monthly earnings in dollars, of a software sales executive is given by where s is the value, in dollars, of the software sold by the executive during the month. Find
A)
B)
C)
D)
E)
where s is the value, in dollars, of the software sold by the executive during the month. Find A)
B)
C)
D)
E)
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8
If is in the domain of , find
A)
B)
C)
D)
E)
is in the domain of , find A)
B)
C)
D)
E)
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9
Find the inverse of , .
A)
B)
C)
D)
E)
, .A)
B)
C)
D)
E)
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10
Assuming that has an inverse function, if find .
A)
B)
C)
D)
E)
has an inverse function, if find .A)
B)
C)
D)
E)
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11
If f is a one-to-one function and
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Use composition of functions to determine whether and are inverses of one another.
and are inverses of one another. فتح الحزمة
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13
Find the inverse of the function below, if one exists.
A)
B)
C)
D)no inverse exists
E)
A)
B)
C)
D)no inverse exists
E)
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14
Use composition of functions to determine whether and are inverses of one another.
and are inverses of one another. فتح الحزمة
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15
Draw the graph of the inverse relation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Draw the graph of the inverse relation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
The function converts a men s shoe size in the United States to the equivalent shoe size in another country. Determine the function that can be used to convert the other country s shoe size to its equivalent U.S. shoe size.
A)
B)
C)
D)
E)
converts a men s shoe size in the United States to the equivalent shoe size in another country. Determine the function that can be used to convert the other country s shoe size to its equivalent U.S. shoe size.A)
B)
C)
D)
E)
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18
Explain how to use the graph of to produce the graph of .
A)Reflect the graph of f across the x-axis.
B)Reflect the graph of f across the x- and y-axes.
C)Shift the graph of f horizontally to the right 1 unit.
D)Shift the graph of f vertically downward 1 unit.
E)Reflect the graph of f across the y-axis.
to produce the graph of .A)Reflect the graph of f across the x-axis.
B)Reflect the graph of f across the x- and y-axes.
C)Shift the graph of f horizontally to the right 1 unit.
D)Shift the graph of f vertically downward 1 unit.
E)Reflect the graph of f across the y-axis.
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19
For , find . State any restrictions on the domain of .
A)
B)
C)
D)
E)
, find . State any restrictions on the domain of .A)
B)
C)
D)
E)
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20
Find .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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21
Write the exponential equation in its logarithmic form.
A)
B)
C)
D)
E)
in its logarithmic form.A)
B)
C)
D)
E)
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22
Find the domain of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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23
Sketch the graph of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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24
The demand d for a specific product, in items per month, is given by where p is the price, in dollars, of the product. What will happen to the demand as the price increases without bound?
A)The demand will approach 0 items per month.
B)The demand will approach items per month.
C)The demand will approach items per month.
D)The demand will approach items per month.
E)The demand will increase without bound.
where p is the price, in dollars, of the product. What will happen to the demand as the price increases without bound?A)The demand will approach 0 items per month.
B)The demand will approach
items per month.C)The demand will approach
items per month.D)The demand will approach
items per month.E)The demand will increase without bound.
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25
Find the domain of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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26
Graph the function below by using its exponential form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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27
Write the equation below in its exponential form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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28
Write the equation below in its logarithmic form. Assume .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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29
The function gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Use a graphing utility to determine how long it will take, to the nearest minute, for the amount of medication in the patient s bloodstream to reach 175 milligrams.
A)14 min
B)2 min
C)21 min
D)39 min
E)9 min
gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Use a graphing utility to determine how long it will take, to the nearest minute, for the amount of medication in the patient s bloodstream to reach 175 milligrams.A)14 min
B)2 min
C)21 min
D)39 min
E)9 min
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30
Evaluate the logarithm without using a calculator.
A)
B)2
C)16
D)
E)3
without using a calculator.A)
B)2
C)16
D)
E)3
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31
Shielding is used to contain radiation. The percentage of a certain radiation that can penetrate x millimeters of shielding is given by How many millimeters of shielding are required so that less than % of the radiation penetrates the shielding? Round to the nearest millimeter.
A)25 millimeters
B)8 millimeters
C)6 millimeters
D)10 millimeters
E)28 millimeters
How many millimeters of shielding are required so that less than % of the radiation penetrates the shielding? Round to the nearest millimeter.A)25 millimeters
B)8 millimeters
C)6 millimeters
D)10 millimeters
E)28 millimeters
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32
Find the domain of the function. Write the domain using interval notation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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33
Shielding is used to contain radiation. The percentage of a certain radiation that can penetrate x millimeters of shielding is given by What percentage of radiation, to the nearest tenth of a percent, will penetrate a shield that is millimeters thick?
A) %
B) %
C) %
D) %
E) %
What percentage of radiation, to the nearest tenth of a percent, will penetrate a shield that is millimeters thick?A)
%B)
%C)
%D)
%E)
% فتح الحزمة
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34
The function gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Find the amount of medication, to the nearest milligram, in the patient s bloodstream after 15 minutes.
A)231 mg
B)182 mg
C)249 mg
D)4 mg
E)15 mg
gives the amount of medication, in milligrams, in a patient s bloodstream t minutes after the medication has been injected into the patient s bloodstream. Find the amount of medication, to the nearest milligram, in the patient s bloodstream after 15 minutes.A)231 mg
B)182 mg
C)249 mg
D)4 mg
E)15 mg
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35
Write the logarithmic equation in its exponential form.
A)
B)
C)
D)
E)
in its exponential form.A)
B)
C)
D)
E)
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36
Evaluate the logarithm below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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37
A cup of coffee is heated to F and placed in a room that maintains a temperature of F. The temperature of the coffee after t minutes is given by . Use a graphing utility to determine when, to the nearest tenth of a minute, the temperature of the coffee will reach F.
A)26.8 min
B)2.9 min
C) min
D)13.6 min
E)42.3 min
F and placed in a room that maintains a temperature of F. The temperature of the coffee after t minutes is given by . Use a graphing utility to determine when, to the nearest tenth of a minute, the temperature of the coffee will reach F.A)26.8 min
B)2.9 min
C)
minD)13.6 min
E)42.3 min
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38
A cup of coffee is heated to 160 F and placed in a room that maintains a temperature of 60 F. The temperature of the coffee after t minutes is given by . Find the temperature, to the nearest degree, of the coffee 45 minutes after it is placed in the room.
A)82° F
B)123° F
C)115° F
D)35° F
E)56° F
. Find the temperature, to the nearest degree, of the coffee 45 minutes after it is placed in the room.A)82° F
B)123° F
C)115° F
D)35° F
E)56° F
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39
Evaluate the logarithm without using a calculator.
A)3
B)-3
C)-2
D)2
E)100
without using a calculator.A)3
B)-3
C)-2
D)2
E)100
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40
The demand d for a specific product, in items per month, is given by where p is the price, in dollars, of the product. What will be the monthly demand, to the nearest unit, when the price of the product is $ .
A) units
B) units
C) units
D) units
E) units
where p is the price, in dollars, of the product. What will be the monthly demand, to the nearest unit, when the price of the product is $ .A)
unitsB)
unitsC)
unitsD)
unitsE)
units فتح الحزمة
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41
Use algebraic procedures to find the exact solution of the equation .
A)3
B)1
C)243
D)7
E)729
.A)3
B)1
C)243
D)7
E)729
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42
Expand the logarithmic expression Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
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43
Write the expression below as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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44
The function models the relationship between the dollar amount x spent on advertising a product and the number of units N that a company can sell. Find the number of units that will be sold with advertising expenditures of $ .
A) units
B) units
C) units
D) units
E) units
models the relationship between the dollar amount x spent on advertising a product and the number of units N that a company can sell. Find the number of units that will be sold with advertising expenditures of $ .A)
unitsB)
unitsC)
unitsD)
unitsE)
units فتح الحزمة
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45
The function models the average typing speed S , in words per minute, of a student who has been typing for t months. What was the student s average typing speed, to the nearest word per minute, after 10 months?
A)29 words/min
B)64 words/min
C)28 words/min
D)29 words/min.
E)67 words/min
models the average typing speed S , in words per minute, of a student who has been typing for t months. What was the student s average typing speed, to the nearest word per minute, after 10 months?A)29 words/min
B)64 words/min
C)28 words/min
D)29 words/min.
E)67 words/min
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46
Use algebraic procedures to find the exact solution(s)of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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47
An earthquake in South America had an intensity of . What did it measure on the Richter scale?
A)1.3
B)7.7
C)2.0
D)17.7
E)5.0
. What did it measure on the Richter scale?A)1.3
B)7.7
C)2.0
D)17.7
E)5.0
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48
A rainstorm in New York City produced rainwater with a pH of 8.1. Determine the hydronium-ion concentration of the rainwater.
A) mol/L
B) mol/L
C) mol/L
D) mol/L
E) mol/L
A)
mol/LB)
mol/LC)
mol/LD)
mol/LE)
mol/L فتح الحزمة
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49
A chemical solution has a hydronium-ion concentration of mole per liter. Determine the pH of the solution.
A)10.7
B)8.8
C)21.5
D)9.3
E)4.6
mole per liter. Determine the pH of the solution.A)10.7
B)8.8
C)21.5
D)9.3
E)4.6
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50
The number of digits N in the expansion of , where both b and x are positive integers, is where denotes the nearest integer less than or equal to Find the number of digits in .
A) digits
B) digits
C) digits
D) digits
E) digits
, where both b and x are positive integers, is where denotes the nearest integer less than or equal to Find the number of digits in .A)
digitsB)
digitsC)
digitsD)
digitsE)
digits فتح الحزمة
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51
How many times as great was the intensity of a South American earthquake, which measured 7.2 on the Richter scale, than a West Coast earthquake, which measured 4.2 on the Richter scale?
A)59,049 times as great
B)1000 times as great
C)52 times as great
D)20 times as great
E)30 times as great
A)59,049 times as great
B)1000 times as great
C)52 times as great
D)20 times as great
E)30 times as great
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52
The function gives the annual interest rate r , as a percent, that a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What interest rate, to the nearest tenth of a percent, will the bank pay on a money market account with a term of 5 months?
A)1.58%
B)2.55%
C)2.06%
D)1.29%
E) %
gives the annual interest rate r , as a percent, that a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What interest rate, to the nearest tenth of a percent, will the bank pay on a money market account with a term of 5 months?A)1.58%
B)2.55%
C)2.06%
D)1.29%
E)
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53
The function models the average typing speed S , in words per minute, of a student who has been typing for t months. Use a graph of S to determine how long, to the nearest tenth of a month, it will take the student to achieve an average typing speed of 68 words per minute.
A)5.6 months
B)7.5 months
C)1.8 months
D)5.2 months
E)1.9 months
models the average typing speed S , in words per minute, of a student who has been typing for t months. Use a graph of S to determine how long, to the nearest tenth of a month, it will take the student to achieve an average typing speed of 68 words per minute.A)5.6 months
B)7.5 months
C)1.8 months
D)5.2 months
E)1.9 months
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54
The function gives the annual interest rate r , as a percent, a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What is the minimum number of complete months during which a person must invest to receive an interest rate of at least 2.3%?
A)17 months
B)10 months
C)19 months
D)16 months
E)8 months
gives the annual interest rate r , as a percent, a bank will pay on its money market accounts, where t is the term (the time the money is invested)in months. What is the minimum number of complete months during which a person must invest to receive an interest rate of at least 2.3%?A)17 months
B)10 months
C)19 months
D)16 months
E)8 months
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55
Evaluate the following logarithmic expression.
A)6
B)9
C)5
D)4
E)1
A)6
B)9
C)5
D)4
E)1
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56
Use the change-of-base formula to graph the logarithmic function below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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57
Expand the given logarithmic expression. Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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58
Write as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.
A)
B)
C)
D)
E)
as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers.A)
B)
C)
D)
E)
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59
Use the change-of-base formula to approximate the logarithm below. Round your answer to four decimal places.
A)-0.3365
B)-0.4854
C)-0.1682
D)0.8271
E)0.6099
A)-0.3365
B)-0.4854
C)-0.1682
D)0.8271
E)0.6099
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60
An earthquake that occurred on the West Coast of the United States had a Richter scale magnitude of 7.6. Find the intensity of this earthquake.
A)39,810,717
B)642,888,893
C)9
D)1998
E)76
A)39,810,717
B)642,888,893
C)9
D)1998
E)76
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61
Estimate the percentage of radioactive material that remains in a sample after 3 years if the half-life of the material is 261 days. Round to the nearest hundredth of a percent.
A)0.42%
B)5.46%
C)0.97%
D)11.92%
E)28.28%
A)0.42%
B)5.46%
C)0.97%
D)11.92%
E)28.28%
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62
A model for how long our coal resources will last is given by where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. If our consumption of coal increases by 14% per year, in how many years will we deplete our coal resources?
A)88 years
B)14 years
C)29 years
D)67 years
E)39 years
where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. If our consumption of coal increases by 14% per year, in how many years will we deplete our coal resources?A)88 years
B)14 years
C)29 years
D)67 years
E)39 years
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63
If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by . Determine the velocity, to the nearest hundredth of a foot per second, of the object after 1.9 seconds.
A)0.07 ft/sec
B)13.75 ft/sec
C)0.16 ft/sec
D)16.93 ft/sec
E)14.84 ft/sec
. Determine the velocity, to the nearest hundredth of a foot per second, of the object after 1.9 seconds.A)0.07 ft/sec
B)13.75 ft/sec
C)0.16 ft/sec
D)16.93 ft/sec
E)14.84 ft/sec
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64
Use algebraic procedures to find the exact solution of the equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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65
Use algebraic procedures to find the exact solution of the equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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66
Use algebraic procedures to find the exact solution of the equation .
A)-1, 13
B)
C)
D)1
E)
.A)-1, 13
B)
C)
D)1
E)
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67
Use algebraic procedures to find the exact solution of the equation
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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68
An industrial psychologist has determined that the average percent score for an employee on a test of the employee s knowledge of the company s product is given by where t is the number of weeks on the job and P is the percent score. Determine the horizontal asymptote of the graph of P .
A)
B)
C)
D)
E)
where t is the number of weeks on the job and P is the percent score. Determine the horizontal asymptote of the graph of P .A)
B)
C)
D)
E)
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69
Use algebraic procedures to find the exact solution(s)of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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70
Use algebraic procedures to find the exact solution of the equation .
A)
B)0, -8
C)9
D)
E)1
.A)
B)0, -8
C)9
D)
E)1
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71
The population P of a city grows exponentially according to the function where t is measured in years. Find the population at time .
A)32,364 people
B)21,280 people
C)10,580 people
D)16,091 people
E)9200 people
where t is measured in years. Find the population at time .A)32,364 people
B)21,280 people
C)10,580 people
D)16,091 people
E)9200 people
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72
The population P of a city grows exponentially according to the function where t is measured in years. When, to the nearest year, will the population reach 15,000?
A)in 5.5 years
B)in 8 years
C)in 3 years
D)in 12 years
E)in 10 years
where t is measured in years. When, to the nearest year, will the population reach 15,000?A)in 5.5 years
B)in 8 years
C)in 3 years
D)in 12 years
E)in 10 years
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73
Use algebraic procedures to find the exact solution(s)of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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74
Find the decay function for the amount of radioactive material that remains in a sample after t days if the half-life of the material is 29 days.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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75
The population of a mid-sized city is growing exponentially. The population of the city was 250,000 in the year 2000 and 273,400 in 2004. Find the exponential growth function that models the population growth of the city. Use to represent the year 2000.
A)
B)
C)
D)
E)
to represent the year 2000.A)
B)
C)
D)
E)
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76
If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds required for an object to reach a velocity v in feet per second is given by . Determine the vertical asymptote for the graph of this function.
A)
B)
C)
D)
E)
. Determine the vertical asymptote for the graph of this function.A)
B)
C)
D)
E)
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77
Use algebraic procedures to find the exact solution of the equation .
A)
B)
C)
D)
E)no solution
.A)
B)
C)
D)
E)no solution
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78
A model for how long our coal resources will last is given by where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. What percent increase in consumption of coal will deplete the resources in 38.1 years? Round to the nearest tenth of a percent.
A)9.9%
B)8.7%
C)10.5%
D)10.1%
E)8.1%
where r is the percent increase in consumption from current levels of use and T is the time (in years)before the resources are depleted. What percent increase in consumption of coal will deplete the resources in 38.1 years? Round to the nearest tenth of a percent.A)9.9%
B)8.7%
C)10.5%
D)10.1%
E)8.1%
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79
An industrial psychologist has determined that the average percent score for an employee on a test of the employee s knowledge of the company s product is given by where t is the number of weeks on the job and P is the percent score. Estimate (to the nearest week)the expected number of weeks of employment that are necessary for an employee to earn a 95% score on the test.
A)35 weeks
B)21 weeks
C)55 weeks
D)6 weeks
E)68 weeks
where t is the number of weeks on the job and P is the percent score. Estimate (to the nearest week)the expected number of weeks of employment that are necessary for an employee to earn a 95% score on the test.A)35 weeks
B)21 weeks
C)55 weeks
D)6 weeks
E)68 weeks
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80
The number of bacteria present in a culture at time t hours is given by . Find the number of bacteria present when .
A)47,500
B)29,687,500
C)237,500
D)9500
E)5,937,500
. Find the number of bacteria present when .A)47,500
B)29,687,500
C)237,500
D)9500
E)5,937,500
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