Question 1

A population N declines by 7% each year.The initial population is 5,056.The population after ​t years is given by ​

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)    A

Question 2

A function shows constant percentage decay.Which of the following may be the graph of this function? ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   D

Question 3

A radioactive substance is decaying at a constant yearly percentage rate of 6%.The initial amount is 444 grams.How much will remain after 13 years? Round your answer to two decimal places if necessary. ​

Accepted Answer

A)  100.68 grams 
B)  198.63 grams 
C)  199.7 grams 
D)  97.68 grams 
A)  100.68 grams 
B)  198.63 grams 
C)  199.7 grams 
D)  97.68 grams B

Question 4

The monthly percentage decay rate for a certain exponential function is 6%.By what percentage does the function decay in a week? (Assume there are four weeks in a month.) Round your answer to two decimal places if necessary. ​

Accepted Answer

A)  1.53% 
B)  1.58% 
C)  0.8% 
D)  1.5% 
A)  1.53% 
B)  1.58% 
C)  0.8% 
D)  1.5%

Question 5

If a function increases by 5% each year, then the yearly growth factor is ​

Accepted Answer

A)  1.05 
B)  5 
C)  0.05 
D)  0.95 
A)  1.05 
B)  5 
C)  0.05 
D)  0.95

Question 6

Next year's value of a certain quantity is 107% of last year's value. ​
Which of the following can you conclude?
​

Accepted Answer

A)  The quantity grows exponentially. 
B)  The quantity grows linearly. 
C)  The quantity decays exponentially. 
D)  The quantity decays linearly. 
A)  The quantity grows exponentially. 
B)  The quantity grows linearly. 
C)  The quantity decays exponentially. 
D)  The quantity decays linearly.

Question 7

The graph of a function that shows constant percentage decay is concave up.

Accepted Answer

A) True 
 B)False

Question 8

If I get a 5% raise each year for four consecutive years, that is the same as a 20% raise.

Accepted Answer

A) True 
 B)False

Question 9

A function   , where t is measured in years, increases by 8% each year.Its initial value is 17.A formula for F is ​

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

The initial value of one function is 31.It has a constant percentage growth rate of 9%.The initial value of a second function is 113.It has a constant percentage decay rate of 10%.If t is the independent variable for both functions, for what value of t are the two functions equal? Round your answer to two decimal places if necessary. ​

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

If a function has constant percentage decrease, then its graph show exponential growth.

Accepted Answer

A) True 
 B)False

Question 12

The half-life of a certain radioactive substance is 5 years.What is the yearly percentage decay rate for this substance? Round your answer to two decimal places if necessary. ​

Accepted Answer

A)  10.65% 
B)  12.94% 
C)  13.87% 
D)  10% 
A)  10.65% 
B)  12.94% 
C)  13.87% 
D)  10%

Question 13

If ​t is increased by 1, then   is decreased by what percentage? ​

Accepted Answer

A)  85% 
B)  15% 
C)  0.85% 
D)  0.15% 
A)  85% 
B)  15% 
C)  0.85% 
D)  0.15%

Question 14

The monthly percentage growth rate for a certain exponential function is 3%.By what percentage does the function grow in a year? Round your answer to two decimal places if necessary. ​

Accepted Answer

A)  43.07% 
B)  42.58% 
C)  35.64% 
D)  36% 
A)  43.07% 
B)  42.58% 
C)  35.64% 
D)  36%

Question 15

Next year's value of a certain quantity is 6% of last year's value. ​
Which of the following can you conclude?
​

Accepted Answer

A)  The quantity grows exponentially. 
B)  The quantity grows linearly. 
C)  The quantity decays exponentially. 
D)  The quantity decays linearly. 
A)  The quantity grows exponentially. 
B)  The quantity grows linearly. 
C)  The quantity decays exponentially. 
D)  The quantity decays linearly.

Question 16

A quantity increases by 7% each month for 11 months.What is the total percentage increase over the 11-month period? Round your answer to two decimal places if necessary. ​

Accepted Answer

A)  76.41% 
B)  110.86% 
C)  110.49% 
D)  77% 
A)  76.41% 
B)  110.86% 
C)  110.49% 
D)  77%

Question 17

The formula for an exponential function is   , where t is measured in months.Then the monthly percentage growth rate for y is ​​

Accepted Answer

A)  1.08% 
B)  8% 
C)  0.08% 
D)  8.02% 
A)  1.08% 
B)  8% 
C)  0.08% 
D)  8.02%

Question 18

An exponential function is a function that shows constant percentage change.

Accepted Answer

A) True 
 B)False

Question 19

If an investment earns interest that is compounded, then the balance will show exponential growth.

Accepted Answer

A) True 
 B)False

Question 20

If a function has constant percentage increase, then its graph shows exponential growth.

Accepted Answer

A) True 
 B)False

Exam 17: Constant Percentage Change

A population N declines by 7% each year.The initial population is 5,056.The population after ​t years is given by ​

A function shows constant percentage decay.Which of the following may be the graph of this function? ​

A radioactive substance is decaying at a constant yearly percentage rate of 6%.The initial amount is 444 grams.How much will remain after 13 years? Round your answer to two decimal places if necessary. ​

The monthly percentage decay rate for a certain exponential function is 6%.By what percentage does the function decay in a week? (Assume there are four weeks in a month.) Round your answer to two decimal places if necessary. ​

If a function increases by 5% each year, then the yearly growth factor is ​

Next year's value of a certain quantity is 107% of last year's value. ​ Which of the following can you conclude? ​

The graph of a function that shows constant percentage decay is concave up.

If I get a 5% raise each year for four consecutive years, that is the same as a 20% raise.

A function , where t is measured in years, increases by 8% each year.Its initial value is 17.A formula for F is ​

If a function has constant percentage decrease, then its graph show exponential growth.

The half-life of a certain radioactive substance is 5 years.What is the yearly percentage decay rate for this substance? Round your answer to two decimal places if necessary. ​

If ​t is increased by 1, then is decreased by what percentage? ​

The monthly percentage growth rate for a certain exponential function is 3%.By what percentage does the function grow in a year? Round your answer to two decimal places if necessary. ​

Next year's value of a certain quantity is 6% of last year's value. ​ Which of the following can you conclude? ​

A quantity increases by 7% each month for 11 months.What is the total percentage increase over the 11-month period? Round your answer to two decimal places if necessary. ​

The formula for an exponential function is , where t is measured in months.Then the monthly percentage growth rate for y is ​​

An exponential function is a function that shows constant percentage change.

If an investment earns interest that is compounded, then the balance will show exponential growth.

If a function has constant percentage increase, then its graph shows exponential growth.

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A population N declines by 7% each year.The initial population is 5,056.The population after t years is given by

A function shows constant percentage decay.Which of the following may be the graph of this function?

A radioactive substance is decaying at a constant yearly percentage rate of 6%.The initial amount is 444 grams.How much will remain after 13 years? Round your answer to two decimal places if necessary.

The monthly percentage decay rate for a certain exponential function is 6%.By what percentage does the function decay in a week? (Assume there are four weeks in a month.) Round your answer to two decimal places if necessary.

If a function increases by 5% each year, then the yearly growth factor is

Next year's value of a certain quantity is 107% of last year's value. Which of the following can you conclude?

A function , where t is measured in years, increases by 8% each year.Its initial value is 17.A formula for F is

The half-life of a certain radioactive substance is 5 years.What is the yearly percentage decay rate for this substance? Round your answer to two decimal places if necessary.

If t is increased by 1, then is decreased by what percentage?

The monthly percentage growth rate for a certain exponential function is 3%.By what percentage does the function grow in a year? Round your answer to two decimal places if necessary.

Next year's value of a certain quantity is 6% of last year's value. Which of the following can you conclude?

A quantity increases by 7% each month for 11 months.What is the total percentage increase over the 11-month period? Round your answer to two decimal places if necessary.

The formula for an exponential function is , where t is measured in months.Then the monthly percentage growth rate for y is