Page 1
1.
For the exponential function given, identify A) the initial value and B) the growth (or
decay) rate.
4,200 2.2x
y=
Enter the growth (or decay) rate as a positive number in percentage form.
2.
Find an exponential function with initial value 3.9 and growth rate 1.2.
Write your answer in
x
y C a=
form.
3.
Find an exponential function with initial value 30 and decay rate 0.1.
Write your answer in
x
y C a=
form.
A)
1.7 2,800x
y=
B)
2,800 2.7x
y=
C)
2,800 1.7x
y=
D)
2.7 2,800x
y=
4.
Find an exponential function,
()fx
, such that
and for every unit increase in
x, the output decreases by 60 percent..
Enter your answer in
x
y C a=
form.
5.
Find an exponential function,
()fx
, such that
(0) 250f=
and for every unit increase
in x, the output increases by 40 percent..
Enter your answer in
x
y C a=
form.
A)
250 1.4x
y=
B)
2.4 250x
y=
C)
1.4 250x
y=
D)
250 2.4x
y=
6.
Complete the description for the exponential function,
320 0.9x
y=
.
For every unit increase in the input, the output increases by ______ percent.
Page 2
7.
Choose the description that best describes the exponential function,
700 0.4x
y=
.
A)
For every unit increase in the input, the output increases by 280,000 units.
B)
For every unit increase in the input, the output increases by 240 percent.
C)
For every unit increase in the input, the output increases by 2.4 percent.
D)
For every unit increase in the input, the output increases by 3.4 percent.
8.
Higher education enrollment in Kentucky for the years from 1985 through 1992 is
displayed in the following table.
Year
85
86
87
88
89
90
91
92
Enrollment
(in thousands)
80
82
85
91
95
105
106
110
Complete the sentence:
Between 1985 and 1990, the enrollment increased by A)___________ thousand students
which is a B)___________ percent increase over the 5 years.
Round answers to 2 decimal places if necessary.
9.
A house valued at $65,000 in 1989 increased in value to $105,000 in 2004
A) What was the absolute change in value?
B) What was the percent change over the 15 years?
Round to 2 decimal places, if necessary.
10.
A house valued at $45,000 in 1989 increased in value to $140,000 in 2001
Choose the true statement.
A)
The value of the house increased approximately 95,000 percent from 1989 to 2001.
B)
The value of the house increased approximately 211 percent from 1989 to 2001.
C)
The value of the house increased approximately 7,917 percent from 1989 to 2001.
D)
The value of the house increased approximately 311 percent from 1989 to 2001.
11.
In 2000, a town’s population was 35,000. In 2010, the population had increased to
100,000. If the town continues to grow at the same rate (Assuming exponential growth),
what will its population be in 2020?
Round your answer to the nearest thousand.
12.
A house valued at $45,000 in 1990 increased in value to $100,000 in 2005.
A) Find a function which gives the value of the house, V, as a function of y, the
number of years after 1990.
Write your answer in
y
V C a=
form and round values to 2 decimal places.
B) Now use that function to predict the value of the house in 2018.
Round to 2 decimal places.
Page 3
13.
In 1923, a year-old Model T automobile was purchased for $750. In 1927, it was worth
$450. (Note: t = 0 in 1922).
Find a function which gives the value of the car, V, as a function of y, the number of
years after 1922, assuming the value of the car depreciated…
A) Linearly. (Write your answer in
V b my=+
form and round values to 2
decimal places.)
B) Exponentially (Write your answer in
y
V C a=
form and round values to 2
decimal places.)
14.
The cost of college tuition increases about 3.2% each year. If the average cost of
tuition is $10,500 in 2007, find a function that gives the average tuition, T, as a function
of the years after 2007, y, (Write your answer in
y
T C a=
form.)
15.
The cost of college tuition increases about 3.2% each year. If the average cost of
tuition is $9,500 in 2007, find:
A) a function that gives the average tuition, T, as a function of the years after 2007, y,
(Write your answer in
y
T C a=
form.) and,
B) use the function to find the average cost of tution in 2012. Round your answer to the
nearest dollar.
16.
What is the growth factor for an object whose mass increases by 22.7% every 3 years?
A)
0.227
B)
1.227
C)
0.773
D)
77.3
17.
What is the decay factor for a business whose profit decreases by 30.5% every 3 years?
A)
0.305
B)
1.305
C)
0.695
D)
69.5
18.
A company states that their annual profit has increased by 695% over the last 12 years
from 1998 to 2010. Write a function to describe the profit with f(0) being 1998 profits
of $186700. Round the growth factor to 3 decimal places if necessary.
Page 4
19.
The function
( )
195400 1.057 T
y=
represents the growth of the deer population in
Wisconsin where T represents 5-year intervals. Create an equivalent function where T
represents 1-year intervals. Round the growth factor to 3 decimal places.
20.
The function
( )
1,979,200 0.917 T
y=
represents the decay of the Asian beetle
population in Wisconsin where T represents 5-year intervals. Create an equivalent
function where T represents 1-year intervals. Round the decay factor to 3 decimal
places.
Page 5
Answer Key