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Unit 7.3 CW: Applications of Exponential Growth & Decay

Total questions: 25

Worksheet time: 2hrs 31mins

Name
Class
Date
1.
Your shiny new boat cost $7650.  The depreciation for your boat is 14% per year. Estimate the value of your vehicle in 3 years. What is the equation that models this problem?
a)
y= 7650(.14)3
b)
y= 7650(.86)3
c)
y= 7650(1+.86/1)3*1
2.
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
3.

Cade earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

4.
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
5.
Solve: 
a)
A
b)
B
c)
C
d)
D
6.

Gasoline costs $3.79 per gallon. If the price per gallon increases an average of 6% per month, which function models the exponential growth of the pricing?

a)

1.06(3.79)t

b)

3.79(1.06)t

c)

[1.06(3.79)]t

d)

3.79(.94)t

7.

Johnny invests money in an account that is continuously compounded using an annual rate of 3%. If his initial investment is $1000, which of the following would model the situation.

a)

A = 1000(1 + 0.03)t

b)

A = 1000e3t

c)
d)

A = 1000e.03t

8.
What does the model P=A(1+r)t best represent?
a)
Exponential growth
b)
Simple Interest
c)
Compound Interest
d)
Exponential Decay
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=5000xx
10.
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
11.

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

12.

What is the initial value for the function: f(x) = 300(1.16)x?

a)

300

b)

1.16

c)

.16

d)

x

13.

Katy deposited $90 in a savings account earning 5% interest, compounded quarterly. Which of the following equations could represent the amount of money in her account yearly?

a)
b)
c)
d)
14.
The population of Hickory NC, can be modeled by P=6191(1.04)t where t is the number of years since 1995. What was the population in 1995?
a)
6191
b)
1
c)
1995
d)
1.04
15.
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
a)
Growth
b)
Decay
16.
Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)3
a)
Growth
b)
Decay
17.
What does the a in y=a(1+r)x  represent?
a)
Time
b)
Rate
c)
Slope
d)
Initial Amount
18.
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
19.

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

20.
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
21.

What is the formula for calculating continuous compounding interest?

a)

A = P * (1 + rt)

b)

A = P * (1 + r/n)^(nt)

c)

A = P * e^(rt)

d)

A = P * (1 + r)^t

22.

If the principal amount is $1000, the interest rate is 5%, and the time period is 3 years, what is the continuous compounding interest?

a)

$150.00

b)

$161.83

c)

$200.00

d)

$250.00

23.

Tritium is a chemical that decays over time. In a sample of tritium, the amount y(in millligrams) remaining after t years is given by the equation below. How much Tritium will be left after 10 years? Round to 2 decimal places. y=10e−0.0562ty=10e^{-0.0562t}  

a)

4.84

b)

5.70

c)

1.32

d)

3.84

24.

Which expression does NOT represent exponential decay?

a)

5(0.86)x5\left(0.86\right)^x  

b)

5e−0.145e^{-0.14}  

c)

  5e0.14x5e^{0.14x}  

d)

5(0.14)x5\left(0.14\right)^x  

25.

A new computer continuously loses about 45% of its value each year. If Monique spent $1600 on her computer, how much will it be worth in 5 years?

a)

$1420.00

b)

$146.31

c)

$65.61

d)

$168.64

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