Deck 17: Constant Percentage Change

Question 1

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. ​

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

Answer 1

1.53%

Question 2

If a function decreases by 7% each year, then the yearly decay factor is ​

A) 1.07
B) 7
C) 0.07
D) 0.93

Answer 2

0.93

Question 3

A quantity decreases by 8% each week for 7 weeks.What is the total percentage decrease over the 7-week period? Round your answer to two decimal places if necessary. ​

A) 55.91%
B) 44.37%
C) 56%
D) 44.22%

Answer 3

44.22%

Question 4

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

Question 5

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. ​

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

Question 6

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. ​

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

Question 7

I got a salary increase of 6% each year for 8 years.What is the total percentage increase in my salary over the 8-year period? Round your answer to two decimal places if necessary. ​

A) 47.01%
B) 60.23%
C) 59.38%
D) 48%

Question 8

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

A)
B)
C)
D)

Question 9

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

Question 10

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

A) 91%
B) 0.09%
C) 1.09%
D) 9%

Question 11

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

Question 12

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

Question 13

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

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

Question 14

A population ​N grows by 8% each year.The initial population is 7,389.The population after ​t years is given by ​

A)
B)
C)
D)

Question 15

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

A)
B)
C)
D)

Question 16

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

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

Question 17

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

Question 18

If the compound interest rate on an investment is small, then the value of the investment will never grow very fast.

Question 19

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

Question 20

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

Question 21

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

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

Question 22

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. ​

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

Question 23

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. ​

A)
B)
C)
D)

Question 24

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. ​

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

Question 25

Over a certain period of time, a precious metal doubled in price every 6 years.What was the yearly percentage growth rate for the price of this metal during this period? Round your answer to two decimal places if necessary. ​

A) 33.79%
B) 12.25%
C) 12.75%
D) 33.33%

Question 26

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

A) ​
B) ​
C) ​
D) ​

Question 27

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

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

Question 28

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

A) ​
B) ​
C) ​
D) ​

Question 29

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

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

Question 30

A population is growing at a constant yearly percentage rate of 7%.The initial population is 570.What will be the population after 14 years? Round your answer to the nearest whole number. ​​

A) 1,157
B) 1,485
C) 1,470
D) 1,129

Question 31

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

A) 0.94%
B) 6.01%
C) 0.06%
D) 6%