# Section 5.2 Growth and Decay

Education

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All Questions

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Multiple Choice

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True False

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Essay

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Short Answer

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Q 1

Solve the differential equation.
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B)
C)
D)
E)

Free

Multiple Choice

B

Q 2

Solve the differential equation.
A)
B)
C)
D)
E)

Free

Multiple Choice

D

Q 3

Solve the differential equation.
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B)
C)
D)
E)

Free

Multiple Choice

D

Q 4

Solve the differential equation .
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B)
C)
D)
E)

Multiple Choice

Q 5

Solve the differential equation.
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B)
C)
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E)

Multiple Choice

Q 6

Write and solve the differential equation that models the following verbal statement:
The rate of change of M with respect to s is proportional to .
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B)
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Multiple Choice

Q 7

Find the function passing through the point with the first derivative .
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Q 8

Find the function passing through the point with the first derivative .
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B)
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Multiple Choice

Q 9

Write and solve the differential equation that models the following verbal statement.Evaluate the solution at the specified value of the independent variable,rounding your answer to four decimal places:
The rate of change of N is proportional to N.When , and when , .What is the value of N when ?
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B)
C)
D)
E)

Multiple Choice

Q 10

The rate of change of N is proportional to N.When and when .What is the value of N when ? Round your answer to three decimal places.
A)1,736.667
B)1,706.667
C)1,656.667
D)59.112
E)5,120.000

Multiple Choice

Q 11

Find the exponential function that passes through the two given points.Round your values of C and k to four decimal places.
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Multiple Choice

Q 12

The isotope has a half-life of 24,100 years.Given an initial amount of 6 grams of the isotope,how many grams will remain after 500 years? After 5,000 years? Round your answers to four decimal places.
A)4.1400 g,3.6374 g
B)3.5486 g,3.1178 g
C)5.9143 g,5.1963 g
D)2.3657 g,2.0785 g
E)7.0972 g,6.2356 g

Multiple Choice

Q 13

The half-life of the carbon isotope C-14 is approximately 5,715 years.If the initial quantity of the isotope is 38 g,what is the amount left after 1,000 years? Round your answer to two decimal places.
A)33.66 g
B)35.76 g
C)34.16 g
D)3.32 g
E)16.83 g

Multiple Choice

Q 14

The isotope has a half-life of 24,100 years.After 1,000 years,a sample of the isotope is reduced to 1.4 grams.What was the initial size of the sample (in grams)? How much will remain after 10,000 years (i.e. ,after another 9,000 years)? Round your answers to four decimal places.
A)1.0086 g,0.7565 g
B)2.3054 g,1.7291 g
C)1.4409 g,1.0807 g
D)2.0172 g,1.5130 g
E)1.8731 g,1.4049 g

Multiple Choice

Q 15

The isotope has a half-life of 5,715 years.After 20,000 years,a sample of the isotope is reduced 0.7 grams.What was the initial size of the sample (in grams)? How large was the sample after the first 2,000 years? Round your answers to four decimal places.
A)7.9172 g,6.2119 g
B)10.2924 g,8.0755 g
C)4.7503 g,3.7271 g
D)6.3338 g,4.9695 g
E)3.9586 g,3.1059 g

Multiple Choice

Q 16

The half-life of the carbon isotope C-14 is approximately 5,715 years.If the amount left after 3,000 years is 1.8 g,what is the amount after 6,000 years? Round your answer to three decimal places.
A)1.251 g
B)1.043 g
C)1.800 g
D)0.604 g
E)2.502 g

Multiple Choice

Q 17

The half-life of the radium isotope Ra-226 is approximately 1,599 years.What percent of a given amount remains after 100 years? Round your answer to two decimal places.
A)95.76 %
B)5.96 %
C)97.76 %
D)3.13 %
E)0.96 %

Multiple Choice

Q 18

The initial investment in a savings account in which interest is compounded continuously is $775.If the time required to double the amount is years,what is the annual rate? Round your answer to two decimal places.
A)9.24 %
B)9.90 %
C)10.82 %
D)8.04 %
E)10.64 %

Multiple Choice

Q 19

The initial investment in a savings account in which interest is compounded continuously is $850.If the time required to double the amount is years,what is the amount after 14 years? Round your answer to the nearest cent.
A)$3,400.00
B)$3,099.86
C)$3,173.33
D)$2,699.86
E)$9,197.18

Multiple Choice

Q 20

Find the principal that must be invested at the rate 8%,compounded monthly,so that $3,000,000 will be available for retirement in 50 years.Round your answer to the nearest cent.
A)$750,000.00
B)$55,681.16
C)$2,151,973.12
D)$1,000,000.00
E)$63,963.69

Multiple Choice

Q 21

Find the time (in years)necessary for 1,000 to double if it is invested at a rate 6% compounded continuously.Round your answer to two decimal places.
A)1.16 years
B)11.55 years
C)1.39 years
D)11.90 years
E)11.58 years

Multiple Choice

Q 22

Suppose that the population (in millions)of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003.Find the exponential growth model for the population by letting correspond to 2000.Round your answer to four decimal places.
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B)
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D)
E)

Multiple Choice

Q 23

Suppose that the population (in millions)of a Paraguay in 2007 is 6.7 and that expected continuous annual rate of change of the population is 0.024.The exponential growth model for the population by letting corresponds to 2000 is .Use the model to predict the population of the country in 2015.Round your answer to two decimal places.
A)7.03 million
B)7.93 million
C)8.32 million
D)8.12 million
E)6.86 million

Multiple Choice

Q 24

The number of bacteria in a culture is increasing according to the law of exponential growth.After 5 hours there are 130 bacteria in the culture and after 10 hours there are 330 bacteria in the culture.Answer the following questions,rounding numerical answers to four decimal places.
(I)Find the initial population.
(II)Write an exponential growth model for the bacteria population.Let t represent time in hours.
(III)Use the model to determine the number of bacteria after 20 hours.
(IV)After how many hours will the bacteria count be 10,000?
A)(I)51.2121 ; (II) ; (III)3,439.1838 ; (IV)30.6439 hr
B)(I)53.3621 ; (II) ; (III)4,813.9010 ; (IV)32.8719 hr
C)(I)51.2121 ; (II) ; (III)2,126.4497 ; (IV)28.3094 hr
D)(I)56.9921 ; (II) ; (III)7,565.3544 ; (IV)34.9831 hr
E)(I)58.5521 ; (II) ; (III)10,217.8179 ; (IV)36.7625 hr

Multiple Choice

Q 25

A container of hot liquid is placed in a freezer that is kept at a constant temperature of .The initial temperature of the liquid is .After 5 minutes,the liquid's temperature is .How much longer will it take for its temperature to decrease to ? Round your answer to two decimal places.
A)5.29 minutes
B)7.94 minutes
C)8.82 minutes
D)3.53 minutes
E)9.70 minutes

Multiple Choice