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Transcript
Unit 5 Test
Part 2 (Exponential Functions)
Directions: Match the equation with the correct graph.
1
1. y = 4(2)x
Name: ______________
Block: ______
A
B
C
D
2. y = -2(3)x
3. y = 3.5(2)x
4. y =
1
-4( )x
2
Directions: Describe each of the following as linear, exponential, or other.
5. f(x) =
1
𝑥
9. f(x) = abx
4
6. f(x) = x + 9
7. f(x) = 5(5)𝑥
1
8. f(x) = 8x3
10. f(x) = ax
Directions: Choose the best answer for each problem.
11. What is the explicit formula for the geometric sequence 6, 24, 96, 384, … ?
a. f(n) = 4(6)𝑛−1
1
b. f(n) = 4(6)𝑛−1
c. f(n) = 6(4)𝑛−1
1
d. f(n) = 6(4)𝑛−1
12. What is the fifth term of the given sequence: f(n) = 3(5)𝑛−1
a. f(3)= 5
b. f(1875)= 5
c. f(1875)=3
d. f(5)=1875
13. The radius of a sphere is given by the equation shown, where V is volume. To the nearest foot, find
the radius of a beach ball that has a volume of 250 cubic feet. Use 3.14 for π.
3𝑉 1
r = (4𝜋)3
a. 2 ft.
b. 3 ft.
c. 4 ft.
d. 9 ft.
14. Which of the following graphs represents an exponential growth function with a y-intercept of 0
and an asymptote at y = -1?
a.
b.
c.
d.
15. The graph of the exponential function f is shown.
For what values of x is f(x) > 24?
a. x > -1
b. -1 < x < 0
c. x > 0
d. ∞ < x < -2
16. The graph of an exponential function is shown.
Which statement about the function is true?
a. The range is the set of all real numbers less than 0.
b. The domain is the set of all real numbers greater than -4.
c. The range is the set of all real numbers greater than 0.
d. The domain is the set of all real numbers less than -4.
17. Based on the table given, which function represents the same relationship?
a. q(x) = (0.25)x
b. q(x) = 256(0.25)x
c. q(x) = 0.0625(4)x
d. q(x) = 0.5(4)x
x
0
1
2
3
y
0.0625
0.25
1
4
Directions: Given the following situation, label each statement as true or false. If it is false, correct the
statement to make it true.
The population of a town over the past 10 years can be represented by the equation:
y = 2450(1.07)x
_____ 18. The initial population was 2400.
_____ 20. The horizontal asymptote is y = 1.07
_____ 19. The growth rate was 7%.
_____ 21. At the end of the first year, the
population was about 2622.
Directions: Answer each question. Make sure to show all work!
22. Write an exponential equation for the functions that contain each of the given points.
I.
(2, 16) and (3, 32)
II.
(2, 4) and (3, 2)
23. A ball is rolling down a slope and continuously picks up speed. Suppose the function
f(x) = 1.2(1.11)x describes the speed of the ball in inches per minute. How fast will the ball be rolling in
10 minutes? Round your answer to the nearest whole number.
24. There are 225 wolves in the state park. The population is increasing at a rate of 15% per year.
Make a prediction for how long it will take the population to reach 500.
25. The value of a car is depreciating at a rate of 5% per year. In 2013, the car was worth $32,000.
Find the value of the car in 2016.
26. Given the function, complete the following table, graph, and questions:
x
f(x)
-1
0
1
2
𝟏
f(x) = 3(𝟐)x
What is the value of a? _____
What is the value of b? _____
What is the y-intercept? _____
What is the domain? _____
What is the range? _____
What is the asymptote? _____
27. An ecologist monitoring a local stream has been collecting samples of an unfamiliar fish species
over the past 4 years and has summarized his data in a table.
a. Find the value of b and state whether it represents exponential
growth or decay.
b. Write the equation that represents the average population per
square mile as a function of years since 2009.
Year
2009
Average
Population
Per Mile
32
2010
48
2011
72
2012
108
2013
2014
c. Predict the average population expected for each year to
complete the table.
d. Graph the data in the table, with 2009 representing year 0.
2015
2016