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Unit6B Exponential Growth and Decay Word Problems

Total questions: 65

Worksheet time: 2hrs 51mins

Name
Class
Date
1.
The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?
a)
y=8(15,000)x
b)
y=15,000(1.08)x
c)
y=15,000(0.92)x
d)
y=15,000(0.08)x
2.
The amount of ibuprofen (medicine for headaches) breaks down by 30% each hour. If a person took a 200 milligram ibuprofen, how much will be left after 3 hours?
a)
5.4 mg
b)
68.6 mg
c)
.0054 mg
d)
2,400,000 mg
3.

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

a)

$5,884.00

b)

$5,178.97

c)

$2,992.96

d)

$2,957.04

4.

The equation y = a(1 - r)x is used for:

a)

1/2 life

b)

Interest

c)

Exponential Growth

d)

Exponential Decay

5.

The equation y = a(1 + r)x is used for:

a)

Exponential Growth

b)

Exponential Decay

c)

Half Life

d)

Interest

6.

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

7.
If 10 mg of iodine 131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.
a)
1.25mg
b)
1.25g
c)
10g
d)
10mg
8.
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
9.

A population of a city is 422,000 and increases by 12% each year. Use an exponential function to find the population of the city after 8 years.

a)

100,144 people

b)

1,083,024 people

c)

1,044,856 people

d)

200,000 people

10.
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
11.
Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)3
a)
Growth
b)
Decay
12.
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
a)
Growth
b)
Decay
13.

You put $2000 in the bank and earn interest at a 2.5% rate compounded annually. How much will you have after 15 years?

a)

$30,758.65

b)

$2,001.56

c)

$2,908.85

d)

$2,896.60

14.

Middletown High School has student elections every year. Lately, the school has seen a 5% decrease in voting from election to election. If 910 students voted this year, how many will be expected to vote 8 years from now? (Round to the nearest whole number if necessary).

a)

604

b)

777

c)

29

d)

198

15.

More and more people are purchasing food from farmers' markets. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 15% each year. If there are 6,200 farmers' markets this year, how many will there be in 10 years? (Round to the nearest whole number if necessary).

a)

25,082

b)

12,937

c)

62,000

d)

43,511

16.

A publishing industry report predicts that magazine subscriptions will drop by 10% each year. If this prediction is correct, then how many subscribers will a magazine with 98,000 subscribers have in 10 years? (Round to the nearest whole number if necessary).

a)

34,170

b)

16,348

c)

7690

d)

76,023

17.

Jenny has $20 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much interest will she earn in 2 years?

a)

$2.05

b)

$45.79

c)

$1.99

d)

$7.51

18.

Lauren has $90 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will she have in 2 years?

a)

$99.23

b)

$21.98

c)

$56.46

d)

$9.21

19.

A cliff overlooking Oak Grove Lake is experiencing erosion, losing elevation at a rate of 5% every millennium. The cliff's current elevation is 1,200 meters. What will its elevation be in 6 millennia? (Round to the nearest whole number if necessary).

a)

882

b)

465

c)

349

d)

975

20.

Kelsey deposited $30 in a savings account earning 10% interest, compounded annually. To the nearest cent, how much interest will she earn in 3 years?

a)

$9.93

b)

$2.01

c)

$17.60

d)

$5.75

21.

Thanks to its environmental initiatives, Silvergrove has cut its annual CO2 emissions by 5%. This year, the town produced 290,000 metric tons of emissions. If the downward trend continues, how much CO2 will be produced 7 years from now? (Round to the nearest whole number if necessary).

a)

202,518

b)

135,792

c)

78,376

d)

20,658

22.

The mice population is 25,000 and is decreasing by 20% each year. What will be the mice population after 3 years?

a)

12,800

b)

15,777

c)

102, 475

d)

2,500

23.

Your new computer cost $1500 but it depreciates in value by about 18% each year. How much will your computer be worth in 6 years? (Round to the nearest cent.)

a)

$456.01

b)

$556.98

c)

$778.22

d)

$332.63

24.

y=3(1.5)xy=3\left(1.5\right)^x  

a)

Growth

b)

Decay

c)

Neither

25.

y=100(5)xy=100\left(5\right)^x  

a)

Growth

b)

Decay

c)

Neither

26.

Evaluate the expression f(x) = 100(0.8)xf\left(x\right)\ =\ 100\left(0.8\right)^x  for f(3).

a)

100

b)

240

c)

51.2

d)

800

27.

In the formula y = a(1±r)t, what does the "a" represent?

a)

The total after the increase or decrease

b)

The initial amount

c)

The Rate of Change

d)

The number of times the change has happened over time

28.

In the formula y = a(1±r)t, what does the "t" represent?

a)

The total after the increase or decrease

b)

The initial amount

c)

The Rate of Change

d)

The number of times the change has happened over time

29.

In the formula y = a(1±r)t, what does the "r" represent?

a)

The total after the increase or decrease

b)

The initial amount

c)

The Rate of Change

d)

The number of times the change has happened over time

30.

If something decays at a rate of 2.5% per hour, what would "t" be over two days?

a)

2

b)

24

c)

48

d)

.025

31.

If something changed at a rate of 3% per week, what would "t" be over a time of one year?

a)

1

b)

7

c)

12

d)

52

32.

Given the function f(x) = 1.07x, how do you know this is an exponential function?

a)

Because the variable is in the exponent

b)

Because the base has a decimal in it

c)

Because f(x) is there

d)

Because my teacher told me

33.

Given the function f(x) = 1.07x, how do you know the exponential function shows growth or decay?

a)

Growth or decay is determined by the value of the base

b)

Growth or decay is determined by the value of the exponent

c)

Because exponential functions are always growth functions

d)

Because exponential functions are always decay functions

34.

Given the function f(x) = 1.07x, is this a growth or decay function?

a)

Growth

b)

Decay

35.

Given the function f(x) = 0.92x, is this a growth or decay function?

a)

Growth

b)

Decay

36.

Given the function f(x) = 0.92x, what is the rate of change?

a)

.92%

b)

9.2%

c)

.08%

d)

8%

37.

Given f(x) = (1.11)18 and the rate of change is 11% every day, how much time has passed?

a)

11 days

b)

18 days

c)

1.11 times 18 days

d)

Underterminable

38.

Given f(x) = (1.0023)36 and the rate of change is 0.23% every hour, how many minutes have passed?

a)

36

b)

60

c)

2160

d)

3600

39.

In 1985, there were 285 cell phone subscribers in Mayville. The number of subscribers increased by 75% per year after 1985. How many subscribers were in Mayville in 2008? (Verbal Question: What word tells us this is growth or decay?)

a)

110,845,988

b)

111, 043,298

c)

109,678,401

d)

110,544,827

40.

The population in Haywardsville is decreasing at a rate of 2.5% per year. If the population in 2000 was 28,000, what will be the expected population in 2015 if this rate of decrease continues? (Verbal Question: How do we know this is growth or decay?)

a)

19,153

b)

19,285

c)

18,956

d)

19,172

41.

The value of a book is $58 and depreciates at a rate of 7% per year. Write an exponential function to find the value of the book after 8 years. (Verbal Question: How do we know this is growth or decay?)

a)

f(t) = 58(0.93)t; $32.46

b)

f(t) = 58(1.07)t; $76.32

c)

f(t) = 58(0.93)t; $34.26

d)

f(t) = 58(1.07)t; $73.62

42.

The population of a small town is 1600 and is increasing at a rate of 3% per year. Write an exponential function to model this situation. Then find the population of the town after 10 years. (Verbal Question: How do we know this is growth or decay?)

a)

f(t) = 1600(1.03)t; 2,150 people

b)

f(t) = 1600(0.97)t; 1,738 people

c)

f(t) = 1600(1.03)t; 2,128 people

d)

f(t) = 1600(0.97)t; 1,819 people

43.

Kimi invests $4,000 at 3% interest compounded continuously. How much money will she have in 4 years?

(a)  

44.

Dash invested $10,000 at 3% interest compounded continuously. How much will he have after 8 years?

(a)  

45.

Damara invests $3500 at 2% compounded continuously for 5 years. How much will she have in her account after 5 years?

(a)  

46.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
47.
Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.
a)
$12712.31
b)
$12,749.30
c)
$12,657.59
d)
$12550.84
48.
Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.
a)
$15,415.94
b)
$15,683.28
c)
$15,927.56
d)
$16,109.05
49.

Willie invests $8,515 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 20 years?

a)

$22,017.32

b)

$23,146.17

c)

$20,021.95

d)

$20,943.52

50.

Jessica invests $3,948 in a savings account with a fixed annual interest rate of 9% compounded continuously. What will the account balance be after 11 years?

a)

$8,786.44

b)

$10,056.40

c)

$10,624.99

d)

$8,357.92

51.

Adam invests $5,208 in a savings account with a fixed annual interest rate of 8% compounded continuously. What will the account balance be after 8 years?

a)

$9,876.87

b)

$10,699.49

c)

$9,489.59

d)

$8,803.91

52.
Change 32% into a decimal.
a)
32
b)
3.2
c)
.32
d)
.032
53.
Convert 3% to a decimal.
a)
.03
b)
.30
c)
.05
d)
.06
54.
Convert 3.5% to a decimal.
a)
3.5
b)
350
c)
.35
d)
.035
55.
Mr. T invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years? 
a)
$15,500.50
b)
$19,260.38
c)
$19,260.40
d)
$21,500.25
56.

What does the P stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year.

57.

What does the r stand for in this formula?

a)

Rate as a percent

b)

Rate as a decimal

c)

number of times interest is compounded

58.

What does the t stand for in this formula?

a)

time in weeks

b)

time in months

c)

time in years

d)

the number of times interest is compounded per year

59.

Jessica invests $3,948 in a savings account with a

fixed annual interest rate of 9% compounded continuously. What will the account balance be after 11 years?

a)

$8,786.44

b)

$10,056.40

c)

$10,624.99

d)

$8,357.92

60.

Sumalee invests $6,227 in a savings account with a

fixed annual interest rate of 8% compounded continuously. What will the account balance be after 6 years?

a)

$10,685.57

b)

$11,011.00

c)

$10,369.77

d)

$10,063.30

61.

Chelsea invests $2,709 in a savings account with a

fixed annual interest rate of 8% compounded continuously. What will the account balance be after 6 years?

(a)  

62.

The formula below can be used to determine the total amount of money in a savings account. What was the initial amount of money deposited in the account?

A=3250e0.062⋅8A=3250e^{0.062\cdot8}  



(a)  

63.

The formula below can be used to determine the total amount of money in a savings account. What is the interest rate as a percent?

A=3250e0.062⋅8A=3250e^{0.062\cdot8}  



(a)  

64.

The formula below can be used to determine the total amount of money in a savings account. How long was the money left in the account?

A=3250e0.062⋅8A=3250e^{0.062\cdot8}  



(a)  

65.

The formula below can be used to determine the total amount of money in a savings account. How much money will end up being in the account if no other deposits or withdrawals are made?

A=3250e0.062⋅8A=3250e^{0.062\cdot8}  



(a)