Free Printable Exponential Growth/Decay 02.28

1.

Which graph shows exponential decay?

a)

b)

c)

d)

2.

A population of humpback whales has 6,500 whales. Their population is declining such that only 94% of the number of whales remain from the year before. Choose the equation that matches this situation:

a)

$y=6,500\left(1.94\right)^x$

b)

$y=6,500\left(94\%\right)^x$

c)

$y=6,500\left(0.94\right)^x$

d)

$y=0.94\left(6,500\right)^x$

3.

The equation that models how much Acetaminophen is in his body is

$y=400\left(0.86\right)^x$

Calculate how much medicine is left after 10 hours

a)

400 milligrams

b)

344 milligrams

c)

89 milligrams

d)

11 milligrams

4.

The population of Townville is decreasing at a rate of 6% each year. If the starting population was 7,000 what equation represents the current population after x number of years?

a)

$f\left(x\right)=7000\left(0.6\right)^x$

b)

$f\left(x\right)=7000\left(0.4\right)^x$

c)

$f\left(x\right)=7000\left(0.06\right)^x$

d)

$f\left(x\right)=7000\left(0.94\right)^x$

5.

A 12 inch candle starts to shrink as it melts. It decreases in height by 3% each hour that it burns. Calculate the height of the candle after 4 hours.

a)

0.88 inches

b)

0.00000972 inches

c)

10.62 inches

d)

7.78 inches

6.

Jamie's Ford F150 truck was purchased for $29,500. Each year it's worth 80% of what it was worth the year before. Choose the equation that gives the truck's value f(x) after any number of years x.

a)

$f\left(x\right)\ =\ 29,500\left(0.8\right)^x$

b)

$f\left(x\right)=0.80\left(29,500\right)^x$

c)

$f\left(x\right)=29,500\left(0.2\right)^x$

7.

You buy a car for $4800. The car depreciation rate is 14.7% annually. Which equation models how much the car would be worth after t years?

a)

$y=4800\left(0.147\right)^t$

b)

$y=4800\left(0.0147\right)^t$

c)

$y=4800\left(0.853\right)^t$

d)

$y=4800\left(1.147\right)^t$

8.

A 78 gram sample of Uranium loses half of its mass each year. How much is left after 6 years?

a)

13 grams

b)

6.5 grams

c)

1.22 grams

d)

592.31 grams

9.

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

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

10.

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

a)

35%

b)

65%

c)

.35%

d)

165%

11.

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

a)

14327

b)

4309

c)

839

d)

7680

12.

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?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

13.

Which of the following models represents exponential decay?

a)

y = 5(1 + .05)^t

b)

y = 5(1 - .05)^t

c)

y = .8(1 + .05)^t

d)

y = -2(1 + .05)^t

14.

Which of the following is an example of exponential decay?

a)

y = 8(.5)^x

b)

y = .8(5)^x

c)

y = 8(5)^x

d)

y = 8(2)^x

15.

Esther purchased a used car, a Ford Focus, for $8400. The car is expected to decrease in value by 20% per year over the next couple of years. What would be the decay factor?

a)

80

b)

20

c)

0.20

d)

0.80

16.

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

a)

$225.00

b)

$123.74

c)

$94.29

d)

$578.27

17.

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

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

18.

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

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

19.

Is this exponential growth or decay?

a)

Growth

b)

Decay

20.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

21.

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

a)

14327

b)

4309

c)

839

d)

7680

22.

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?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

23.

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?

a)

9766

b)

9006

c)

9765

d)

5433

24.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

25.

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

a)

.6

b)

1.06

c)

1.6

d)

.4

26.

Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. What is the growth factor?

a)

.96

b)

1.4

c)

1.04

d)

$3000

27.

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

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

28.

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?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

29.

Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)^x, where x is the number of years since January 1980. What is the was the population of Brownville in 1980?

a)

102.2 people

b)

720,500 people

c)

1.022 people

d)

1022 people

30.

Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. If no other money is added or withdrawn from the account, how much will be in the account after 10 years?

a)

$3122.18

b)

$4994.50

c)

$4440.73

d)

$86,776.40

31.

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?

a)

356

b)

265

c)

5825

d)

1329

32.

In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?

a)

OVERFLOW

b)

1994

c)

1000

d)

43871

33.

You buy a new computer for $2100. The computer decreases by 50% annually. How much is it worth after 2 years.

a)

225

b)

325

c)

425

d)

525

34.

The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city.
Every year the population drops by 4.5%. What is the population after 3 years?

a)

1,069 people

b)

894 people

c)

816 people

d)

854 people

35.

The city of Whoville has been much more stable since the Grinch turned his life around. The population of 900 is increasing at a rate of 7.5% per year. If the population continues growing at the same rate, how many people will there be in 11 years?

a)

424288

b)

1994

c)

10642

d)

900

36.

The Country of Puerto has 3,370,000 people in it and is decreasing at a rate of 4.5%. Estimate the population after 40 years.

a)

534,275

b)

19,601,148

c)

1,350,756

d)

2,521,541

37.

If the decay rate is 20%, which of the following represent the decay factor?

a)

0.2

b)

0.8

c)

1.2

d)

1.8

38.

If the growth rate is 80%, what is the growth factor?

a)

0.2

b)

0.8

c)

1.2

d)

1.8

39.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

40.

Jack invest $600 earning 5% interest rate. How much will he have after 5 years?

a)

$630

b)

$729.30

c)

$765.77

d)

$4556.25

41.

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

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

42.

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

a)

Growth

b)

Decay

43.

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

a)

Growth

b)

Decay

44.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

45.

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

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

46.

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

a)

14327

b)

4309

c)

839

d)

7680

47.

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?

a)

9766

b)

9006

c)

9765

d)

5433

48.

Classify the model as Exponential GROWTH or DECAY.

$A=10(1.01)^3$

a)

Growth $y=a\left(1+r\right)^t$

b)

Decay $y=a\left(1-r\right)^t$

49.

Classify the model of an Exponential GROWTH.

a)

$y=a\left(1+r\right)^t$

b)

$y=a\left(1-r\right)^t$

50.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

51.

How do you know that this was exponential decay? $f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$

a)

Because the 25 was bigger than one

b)

Because the 0.20 was bigger than one

c)

Because the 25 was less than one

d)

Because the 0.20 was less than one

52.

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

a)

y=5000(1 - 0.30)^x

b)

y=30(5000)^x

c)

y=5000(1 + 0.30)^x

d)

y=5000x^x

53.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

54.

Change 11.2% to a decimal.

a)

11.2

b)

1.12

c)

0.112

d)

0.0112

55.

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?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

56.

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

a)

.6

b)

1.06

c)

1.6

d)

.4

57.

What is the growth rate in the function f(x)=2(1.44)^x

a)

144%

b)

2%

c)

44%

d)

X%

58.

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

a)

35%

b)

65%

c)

.35%

d)

165%

Exponential Growth/Decay 02.28

Total questions: 58

Worksheet time: 3hrs 16mins

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