Exponential Functions – Test C
NAME:_________________________
1. In 1995, there were 285 cell phone subscribers in the small town of Gateway. The number of
subscribers increases by 30% per year after 1995. (Round to the nearest whole number when doing
all calculations.)
a. Make a table showing the number of cell phone subscribers in Gateway for the six years after 1995.
Number of years
since 1995
Cell phone
subscribers
0
1
2
3
4
5
6
b. Which of the following scatterplots could be a plot of the (year, subscribers) data for the first few
years?
c) Write a rule beginning “y =…” that could be used to calculate the number of subscribers for any
number of years. Then write a recursive rule. Explain each of the numbers used in your rule in the
box provided.
d) How many subscribers would you expect there to be after 20 years? Write the equation you used
to find the answer in the box provided.
e) If the local cell tower can only handle 70,000 subscribers, when would you predict an additional
cell tower will be needed?
2. The following table gives the number of AIDS cases reported in the Los Angeles area for the years
1983 through 1988.
Years since 1983 (x) 0
1
2
3
4
5
Number of AIDS Cases Reported (y) 224
356
567
901
1434
2280
a. Use your calculator to produce a scatterplot, an equation for a linear model, and an equation for
an exponential model. Round to two decimal places.
Linear model: __Y =___________________ Exponential model:___Y=______________________
b. Which model, linear or exponential, do you think would be a better predictor of the number of
AIDS cases in Los Angeles at the end of the 1990s and beyond?
c. For the model you chose in part b, explain what the numbers represent in the context of the
problem.
d. Determine the number of AIDS cases reported in year 7.
e. Determine the year that the number of AIDS cases will reach 10000.
3.
Use the following table to answer questions below.
No. of
Bounces
Rebound
Height in
inches
0
1
2
3
4
5
501
275.6
151.6
83.4
45.8
25.2
a. What is the initial height that the ball is dropped from? _________________
b. What is the growth/decay factor or “b” term? _________________________
c. Write an equation or rule for this pattern. ____________________________
d. What will the height be on the seventh bounce? _______________________
4. Suppose a hospital patient receives a 350 mg. injection of medication. The medication
metabolizes in the blood so that only 60% of the medication from the previous hour remains in the
blood after each hour.
a. Complete the following table showing the amount of medication in the blood stream after each
hour. (Round to the nearest tenth.)
0
1
2
3
4
5
Hours since Injection
6
Medication Remaining in mg.
b. Write a “y = “ rule and a recursive rule that can be used to calculate the amount of medication
remaining in the blood at any hour (measured in milligrams).
c. What amount of medication remains in the blood after 5.5 hours?
d.
When will the amount of medication remaining be half of the original amount of medicine
injected. Give your answer to the nearest tenth.
5. Identify if the table below represents exponential growth or decay. Then write the recursive
rule and the “y =” rule for the data without typing the data into your calculator.
0
x
1
50
y
2
65
3
84.5
4
109.85
5
6
142.805 185.6465 241.34045
6. Identify if the table below represents exponential growth or decay. Then write the recursive
rule and the “y =” rule for the data without typing the data into your calculator.
0
x
y
50
1
30
2
18
3
4
10.8
6.48
5
3.888
6
2.3328
7.
A baseball card bought for $50 increases 3% in value each year. Write a “y = “ rule that
models the value of the baseball card. Find the value of the card in 15 years.
8. A new car that sells for $18,000 depreciates 25% each year. Write a “y = “ rule that models
the value of the car. Find the value of the car in 6 years.
9. A hospital prepares a 100 mg supply of technetium-99m which decays at a rate of 10.9% per
hour.
a. Write an equation that models this situation.
b. How much technetium-99m would be in a person’s system after 3 hours?
c. Using your model estimate the half-life of technetium-99m to the nearest tenth.