Free Printable Exponential Decay

Worksheets

Exponential Decay

Total questions: 19

Worksheet time: 2hrs 25mins

Name

Class

Date

A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population. Which function can be used to determine the number of deer, y, in this population at the end of t years?

y = 1500(1 - 0.015)^t

y = 1500(0.015)^t

y = 1500(1 + 0.015)^t

y = 1500(1.5)^t

The graph represents an exponential growth situation.

Eventually, the car will be worth exactly $0.

The starting value of the car was $12,000.

The range for the situation is y ≥ 0.

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 14.9% per minute. Which function can be used to model the number of bacteria in the colony after x minutes?

f(x) = 12000(1 + 14.9)^x

f(x) = 12000(1 - 14.9)^x

f(x) = 12000(1 + 0.149)^x

f(x) = 12000(1 - 0.149)^x

Some banks charge a fee for a savings account that is left inactive for an extended period of time. The equation y = 5000(0.98)^x represents the amount remaining, y, of one account that was left inactive for a period of x years. What does the number 5000 represent in this situation?

A fee charged for an inactive account

The percent of money in the account after x years

The amount of money in the account initially

The amount of money in the account after x years

A child asks her dad for an allowance that starts with a penny and then doubles every day for a month. Which function can be used to model the amount of money, A, the child will receive each day, x?

A(x) = 2(0.01)^x

A(x) = 0.01(2)^x

A(x) = 0.01(1 - 2)^x

A(x) = 2(1.01)^x

The number of players decreases by 30% each round.

The range for the function is 1 < y < 5.

The domain for the function is 5 < x < 65.

The situation represented is exponential decay.

The function to find the value of a car after t years is given by v(t) = 24,000(.75)^t Which of the following statements is not true?

The starting value of the car was $24,000.

The y-values of the graph increase as the x-values increase.

The value of b indicates this is an exponential decay situation.

The horizontal asymptote is y = 0, which means the car will never have a value of $0.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

^.08

^1.08

.92

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

Growth

Decay

10.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

Growth

Decay

11.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

y=5000(0.7)^x

y=30(5000)^x

y=5000(1.3)^x

y=5000x^x

12.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

14327

4309

839

7680

13.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

$23,219.72

$136.72

$51,710.94

$16,710.94

14.

The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.

323.945

333.955

325.395

324.954

15.

The half-life of a certain radioactive material is 71 hours. An initial amount of the material has a mass of 722 kg. Find how much radioactive material remains after 17 hours.

About 612 kg

About 600 kg

About 622 kg

About 619 kg

16.

A bicycle depreciates at a rate of 15%. Therese bought a bicycle for $250. How much should it be worth 6 years later?

About $94

About $90

About $104

About $89

17.

A boat costs $15,500 and decreases in value by 10% per year. How much will the boat be worth after 5 years?

$9,153

$15,450

$8,237

$155

18.

Which investment would be worth the most after 20 years? A) An initial investment of $3000 compounded annually at a rate of 12% after 20 years. B) An initial investment of $3000 compounded quarterly at a rate of 11.9% after 20 years. C) An initial investment of $3000 compounded continuously at a rate of 11.8% after 20 years.

19.

The function f(x) = 50(0.972)^x , where x is the time in years, models a declining feral cat population. How many feral cats will there be in 4 years?

About 204 feral cats

About 51 feral cats

About 194 feral cats

About 45 feral cats

100 %

Exponential Decay

Total questions: 19

Worksheet time: 2hrs 25mins

Similar Resources on Wayground