Exponential Functions Unit Assessment
KEY
Form A
Show all of your work and evidence, to support your answers.
1. The city of Vancouver’s population in 2010 was 160,000. Every year Vancouver’s
population grows by 2%.
a) Write a function g(x) that models the situation above. Define both x and g(x).
g(x) = 160,000(1.02)x where x is the number of years since 2010 and g(x) is the total
population.
OR
g(x) = 160,000(1.02)x-2010 where x is the year and g(x) is the total population.
b) Find g(5) and write your answer in function notation rounded to the nearest whole
number.
g(5) = 160,000(1.02)5 = 176,653
c) Write your answer from part b in a complete sentence (make sure to relate it to the
given situation).
In the year 2015, which is 5 years after 2010, the total population of Vancouver
will be 176,653 people.
Answer needs to include:
 Reference to the input value of 5
 Reference to the output value given in part b
d) In what year will the population exceed 190,000?
□
□
□
□
2008
2009
2018
2019
e) If the population continues to grow at the same rate, predict what the population will
be in the year 2025.
□
□
□
□
193,000
215,500
262,500
2,465,000
Algebra 1 by Southwest Washington Common Core Mathematics Consortium is licensed
under a Creative Commons Attribution 4.0 International License 2013-14
Page 1 of 5
Exponential Functions Unit Assessment
KEY
Form A
2) After a dog or cat is given a preventative flea medicine, the medicine begins to break down in the
animal’s bloodstream. With each passing hour, there is less active medicine in the blood. This
situation can be represent by the function f (x)  20(0.6) x , where f(x) is the amount of medicine
(measured in mg) and x is the number of hours.
Complete the table. Then graph the exponential function using the completed
table of values.
b)
a)
x
f (x)  20(0.6) x
0
20
1
12
2
7.2
3
4.32
4
2.592
5
1.5552
6
0.93312
Answer the following questions that relate to the given situation.
c) What is the initial amount of medicine? 20 milligrams
d) Is the function growing or decaying? decaying
e) What is the range of the function? All positive real numbers less than or equal to 20.
f) Why does your range from (e) above make sense for this situation?
The initial dose is 20 milligrams, which is the highest level in the animal’s
bloodstream. Then the amount decreases. The lowest is gets is really close to zero,
but it never mathematically reaches zero.
g) What is the percent increase/decrease of the function? Decreasing at a rate of 40%
f) Estimate the half-life of this medication. The half-life is 1.36 hours. Accept answers between 0.1
and0.5 hours.
h) Jake uses a different flea medication represented by the function d(h)  60(0.8)h . He
says the medicine is decaying at a rate of 80%. Is Jake correct or not? Justify your
answer.
Jake is not correct. The (0.8) in the equation represents how much medicine is left
Page 2 of 5
Exponential Functions Unit Assessment
KEY
Form A
remaining in the animal, not the rate at which the medicine is decaying. Jake’s flea
medication has a decay rate of 20%.
Page 3 of 5
Exponential Functions Unit Assessment
KEY
Form A
For the following questions, use the Representations of Different Functions on page 4.
2. Place a check next to your answers for each of the following questions. Keep in
mind that:
 Each function may be checked more than once.
 Every question may have more than one function as an answer.
g(x)
Identify which
A functions are decaying
functions.
Identify which
B functions have a yintercept at (0, 2).
Identify which
functions do not
C
represent an
exponential function.
Identify which
D functions are changing
at a rate of 2%.
k(x)
n(x)
m(x)
a(x)
X
X
p(x)
h(x)
f(x)
j(x)
X
X
X
X
X
X
X
E Which of the following functions below
gives an output of 8 when the input is 1?
□ p(x)
□ f(x)
□ a(x)
□ h(x)
H Which of the following functions is
growing twice as fast as p(x) ?
□ g(x)
□ h(x)
□ f(x)
□ n(x)
F
I
Which of the following functions has the
fastest growth? (only check one)
□ p(x)
□ h(x)
□ f(x)
□ n(x)
Check the two functions below that
represent equivalent functions.
□ m(x)
□ n(x)
□ a(x)
□ j(x)
G Which of the following functions has a
range of y > -3?
□ g(x)
□ f(x)
□ a(x)
□ j(x)
Page 4 of 5
Exponential Functions Unit Assessment
KEY
Form A
Representations of Different Functions
(use these functions to answer question #3 on page 3)
g(x)
k(x)
m(x)
n(x)
x
k(x)
0
5
1
9
2
13
3
17
n(x)  5(1.02)x
a(x)
p( x)  5(2) x
m(x)  5(0.98)x
h(x)
p(x)
f(x)
j(x)
x
h(x)
x
j(x)
1
8
0
5
2
32
1
4.9
3
128
2
4.802
4
512
3
4.706
Page 5 of 5