Free Printable Exponential Decay and Growth

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Exponential Decay and Growth

Total questions: 40

Worksheet time: 1hrs 3mins

Name

Class

Date

What is the initial value for the exponential function:

f(x) = 300(1.16)^t?

300

1.16

.16

Is this exponential growth or decay?

Growth

Decay

What does the model P=A(1+r)^t best represent?

Exponential growth

Simple Interest

Compound Interest

Exponential Decay

What type of function is f(x)=2(0.05)^x ?

Exponential Growth

Linear

Exponential Decay

None of the Abovee

A new savings account is opened with $400 and gains 3% every year. What's the amount after 5 years?

$415

$463.71

$343.49

$460.12

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

A city has a population of 21,517 based on a census taken in 1998. If the population is expected to grow by 11% annually, what will the population be in the year 2030?

606,900

517

492,573

None of these

Give the rate of decay:
y = 35(0.65)^x

35%

65%

.35%

165%

Use the function, M=.05(2)^t, where M is the amount of money you have after t days.
How much money will you have after 14 days?

$ 819.20

$ 8,192.00

$ 1.40

$ 819.02

10.

Use the function, M=.05(2)^t, where M is the amount of money you have after t days.

What is the y-intercept? OR What is the starting number, “a”?

(0, .05)

(0,2)

(0, .1)

(0,0)

11.

Use the function, N = 14,000(.96)^t.
Is the function INCREASING or DECREASING?

Increasing

Decreasing

12.

A stamp gets more expensive each year. It increases in value by 60 % each year. What is the GROWTH FACTOR?

1.06

1.6

13.

A stamp gets more expensive each year. It increases in value by 60 % each year. What is the GROWTH RATE?

0.06

0.6

1.6

14.

What is the x-intercept of the exponential function?

(0,1)

(0,0)

There is not one

15.

The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year?

hint: how many months are in a year?

356

265

5825

1329

16.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

9766

9006

9765

5433

17.

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

Growth

Decay

18.

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

Growth

Decay

19.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

y = 15(35)^x

y = 15(1.35)^x

y = 15(0.35)^x

y = 35(1.15)^x

20.

Anything raised to a power of zero is always:

itself

negative

21.

A population has a growth/decay factor of 1.045 What is happening to the population?

It grows at a rate of 45%

It grows at a rate of 4.5%

It dies at a rate of 45%

It dies at a rate of 1045%

22.

A population has a growth/decay factor of 0.90. What is happening to the population?

It grows at a rate of 90%

It dies at a rate of 90%

It grows at a rate of 10%

It dies at a rate of 10%

23.

What is the growth or decay rate for the following equation?
y = 1/3(0.7)^x

7% decay

70% decay

30% growth

30% decay

24.

What is the growth or decay rate for the following equation?
y = 2.5(1.15)^x

-15% decay

115% growth

15% growth

25% growth

25.

Which of the following equations has a growth rate of 50%

y = 2(0.50)^x

y=3(1.5)^x

y=1.2(2.5)^x

All of the equations show growth of 50%

26.

Which of the following equations has a decay rate of 20%

y = 2(0.80)^x

y=2(1.20)^x

y=2(.20)^x

None of the equations show decay of 20%

27.

James' a 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.

70(2)³⁵

70(2)⁵

2(70)⁵

5(70)²

28.

The value of a painting is $12,000 in 1990 and increases by 8% of its value each year. Write and evaluate an expression to estimate the paintings value in 2005.

1.08(12,000)^t = $36,000

12,000(1.08)^t = $38, 066

12,000(0.5)^t = $10,000

12,000(0.92)^t= $40,000

29.

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

30.

Use the function, N = 14,000(.96)^t.
What is the Initial Amount?

14,000

.96

31.

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

32.

What is the starting term for the function: f(x) = 800(0.85)^x?

what is the value for “a”?

800

0.85

0.15

33.

A 78 gram sample of Uranium loses half of its mass each year. What is the exponential equation?

y=78(0.5)^x

y=78(1.5)^x

y=78(2)^x

34.

Solve for x.
5^x = 1

-1

35.

You have a boat worth $85,340 new. It depreciates by 25% of its value each year. It has been 48 months since you bought the boat. How much is it now worth?

hint: first think - how many years are 48 months?

$27,002

$333

$72,480

$14,943

36.

When do we have growth?
f(x) = (a)(b^x)

a < 1

b > 1

0 < b < 1

a > 1

37.

When does the exponential function show a decay, downward curve? f(x) = a(b)^x.

a < 1

b > 1

b < 1

a > 1

38.

Write the equation that represents the table below:

y=0.5(4)^x

y=2(4)^x

y=4(2)^x

y=4(0.5)^x

39.

Is the pictured graph growth, decay, or linear or none?

Exponential Growth

Exponential Decay

Linear

None

40.

Is the pictured graph growth, decay, or linear or none?

Exponential Growth

Exponential Decay

Linear

None

100 %

Exponential Decay and Growth

Total questions: 40

Worksheet time: 1hrs 3mins

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