Deck 16: Exponential Growth and Decay

Question 1

For a function that shows exponential decay, an increase of 1 unit in the variable causes the function to be divided by the decay factor.

Answer 1

False

Question 2

A radioactive substance is decaying exponentially with yearly decay factor 0.91.What is the decade decay factor? Round your answer to two decimal places. ​

A) 0.09
B) 0.99
C) 9.10
D) 0.39

Answer 2

0.39

Question 3

If there are G grams of a certain radioactive substance present today, then in one year there will be grams remaining.There are initially 29 grams present.Find a formula that gives the amount G, in grams, remaining after t years. ​

A) ​
B)
C) ​
D) ​

Answer 3

Question 4

If the population of a certain town today is N, then in one year the population will be .The initial population is 3,132.Find a formula that gives the population N after t years. ​

A)
B) ​
C)
D) ​

Question 5

A graph showing exponential decay is concave down.

Question 6

Exponential functions are functions with a constant proportional change.

Question 7

A certain function is an exponential function of time.The weekly growth factor is 1.51.What is the monthly growth factor? (Assume there are four weeks in a month.) Round your answer to two decimal places. ​

A) 0.38
B) 1.11
C) 5.20
D) 6.04

Question 8

The population of a certain town is growing exponentially with yearly growth factor 1.03.The initial population is 1,874.What will be the population after 6 years? Round your answer to the nearest whole number. ​

A) 2,056
B) 2,238
C) 1,868
D) None of the above

Question 9

A graph showing exponential growth is concave up.

Question 10

The graph of exponential growth is decreasing.

Question 11

A certain function is an exponential function of time.The yearly growth factor is 1.47.What is the decade growth factor? Round your answer to two decimal places. ​

A) 0.15
B) 1.04
C) 47.12
D) 14.70

Question 12

A population P grows so that we can always get next year's population from this year's population by multiplying by 1.52.The initial population is 569.The population after t years is given by ​

A)
B)
C)
D)

Question 13

If there are G grams of a certain radioactive substance present today, then in one year there will be grams remaining.There are initially 28 grams present.How much remains after 6 years? Round your answer to two decimal places. ​

A) 25.94 grams
B) 23.32 grams
C) 22.18 grams
D) None of the above

Question 14

The decay factor of an exponential function is 0.74.The initial value is 1.5.Then a formula for P is ​

A) ​
B) ​
C) ​
D)

Question 15

The formula for an exponential function is .Then the growth factor is: ​

A) 127
B) 2.75
C) t
D) Y

Question 16

The growth factor of an exponential function is 2.42.The initial value is 3.78.Then a formula for P is ​

A) ​
B) ​
C) ​
D)

Question 17

The formula for an exponential function is .Then the initial value is: ​

A) 32
B) 136.32
C) t
D) 4.26

Question 18

The formula for an exponential function is .Then the decay factor is: ​

A) 632
B) Y
C) t
D) 0.66

Question 19

A certain function is an exponential function of time.The monthly growth factor is 1.5.What is the weekly growth factor? (Assume there are four weeks in a month.) Round your answer to two decimal places. ​

A) 0.38
B) 1.11
C) 5.06
D) 6.00

Question 20

For a function that shows exponential growth, an increase of 1 unit in the variable causes the function to be multiplied by the growth factor.

Question 21

The initial value of an exponential function is 16, and the growth factor is 1.02.If t is the independent variable, for what value of t does the function have the value 46? Round your answer to two decimal places. ​

A) ​
B) ​
C) ​
D)

Question 22

A population is growing exponentially with a weekly growth factor of 1.03.What is the yearly growth factor? Round your answer to two decimal places. ​

A) 0.02
B) 1.00
C) 53.56
D) 4.65

Question 23

Solve the equation .Round your answer to two decimal places. ​

A) ​
B) ​
C)
D) ​

Question 24

Next year's value of quantity 1 is obtained by multiplying this year's value of quantity 1 by 1.13.Next year's value of quantity 2 is obtained by adding 1.13 to this year's value of quantity 1.Which of the two quantities are growing exponentially? ​

A) Only quantity 1
B) Only quantity 2
C) Both quantity 1 and quantity 2
D) Neither quantity 1 nor quantity 2

Question 25

Solve the exponential equation .Round your answer to two decimal places. ​

A) ​
B) ​
C)
D) ​

Question 26

Select the graph of . ​
​

A) ​
​
B) ​
​
C) ​ ​
D) ​

Question 27

A population is growing exponentially with a yearly growth factor of 1.24.What is the monthly growth factor? Round your answer to two decimal places.

A) 0.10
B) 1.02
C) 14.88
D) 13.21

Question 28

Next year's value of quantity 1 is obtained by multiplying this year's value of quantity 1 by 0.75.Next year's value of quantity 2 is obtained by adding 0.75 to this year's value of quantity 1.Which of the two quantities are decaying exponentially? ​

A) Only quantity 1
B) Only quantity 2
C) Both quantity 1 and quantity 2
D) Neither quantity 1 nor quantity 2

Question 29

The initial value of one exponential function is 40, and the growth factor is 1.05.The initial value of a second exponential function is 90, and the decay factor is 0.95.If is the independent variable for both functions, for what value of t are the two functions equal? Round your answer to two decimal places. ​

A) ​
B)
C)
D)

Question 30

Over a certain time period the price of gold doubled every 4 years.What was the yearly growth factor for gold during this period? Round your answer to two decimal places. ​

A) 2.00
B) 1.19
C) 1.69
D) None of the above

Question 31

The half-life of a certain radioactive substance is 9 years.What is the yearly decay factor? Round your answer to two decimal places. ​

A) 4.50
B) 1.56
C) 0.93
D) None of the above

Question 32

Solve the inequality .Round your answer to two decimal places. ​

A) ​
B) ​
C) ​
D) ​

Question 33

Next year's value of a certain quantity is obtained by multiplying this year's value of the quantity by 1.71.Which of the following can you conclude? ​

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

Question 34

Solve the inequality .Round your answer to two decimal places. ​

A) ​
B)
C) ​
D) ​

Question 35

A radioactive substance is decaying exponentially with yearly decay factor 0.93.What is the monthly decay factor? Round your answer to two decimal places. ​

A) 0.08
B) 0.99
C) 11.16
D) 0.42

Question 36

Solve the equation .Round your answer to two decimal places. ​

A) ​
B) ​
C)
D) ​

Question 37

For a certain substance, we get next week's amount by dividing by 5.That means the amount is showing exponential decay.What is the weekly decay factor? Round your answer to two decimal places. ​

A) 0.20
B) 5.00
C) 1.19
D) None of the above

Question 38

Select the graph of . ​
​

A) ​
​
B) ​
​
C) ​
D) ​

Question 39

Next year's value of a certain quantity is obtained by multiplying this year's value of the quantity by 0.74.Which of the following can you conclude? ​

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

Question 40

Solve the exponential equation .Round your answer to two decimal places. ​

A) ​
B) ​
C)
D) ​

Question 41

Solve the inequality . ​

A) ​
B) ​
C)
D) ​