Download Exponential Relationships

Name ________________________________________ Date __________________ Class __________________
Exponential Relationships
UNIT
6
Practice Test
1. Which exponential function matches the
values in the table below?
x
1
2
3
f(x)
−18
162
−1458
A f(x) =
6. Does each set of ordered pairs satisfy an
exponential function?
A {(1, 2), (2, 6), (3, 18), (4, 54)}
Yes
1
(−18)x
2
No
B {(1, −2), (2, 4), (3, −6), (4, 8)}
B f(x) = 2(−9)x
Yes
C f(x) = −2(3)2x
No
C {(−2, 1), (−8, 2), (−32, 3), (−128, 4)}
D f(x) = −18x
2. What are the next two terms in the
sequence −9, 3, −1, …?
Yes
No
D {(−1, 2), (0, −10), (1, 50), (2, −250)}
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Yes
3. The first term of a geometric sequence
is −10 and the common ratio is 4. Write
the explict rule of the sequence and find
the fifth term of the sequence.
No
For 7–9, solve for x.
7.
2 x
6 = 864
3
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8. 6(7)x = 2058
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4. Write an equation for an exponential
function that includes the points (3, 18)
and (4, 54).
x
3⎛5⎞
125
9. ⎜ ⎟ =
5⎝9⎠
2187
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10. A new movie premiered on Friday,
September 2, and 1350 people attended.
Attendance then decreased by 20% each
day. Write an exponential decay function
to model this situation. Then find the
attendance on September 7.
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5. Which of the following regression
equations could represent a town with an
initial population of 875 people and an
annual growth rate of approximately 2%?
A y = 875 i 1.02x
B y = 875(1.02)x
C y = 875(2)
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x
________________________________________
D y = 875x1.02
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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Name ________________________________________ Date __________________ Class __________________
UNIT
6
Exponential Relationships
Practice Test
11. a. Graph y = 3x and y = 3x + 4.
13. Use the parent function f(x) = 2.5x.
a. Complete the table.
f(x) = 0.5(2.5)x
x
−2
−1
0
1
2
x
b. Compare the graphs of y = 3 and
y = 3x + 4.
b. Add the graph of the translation to the
graph of the parent function.
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____________________________________
____________________________________
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12. Alistair has $900 in his savings account.
He is looking at two investment plans.
Under Plan A, he will increase his
account balance by $250 a year. Under
Plan B, he will increase his account
balance by 25% each year.
c. Describe the end behavior and find
the y-intercept of the new graph.
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14. The table shows the population y of a
town over a period of time.
a. Write equations to represent the
money Alistair would have under
Plan A and Plan B.
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____________________________________
b. To the nearest penny, how much
more under Plan B would Alistair
save than under Plan A after 5
years?
Year
Population
0
6915
1
2
7285
7780
3
8293
4
8701
5
9284
6
9816
Write an exponential regression function
for the data. Round to the nearest
hundredth.
____________________________________
_________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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Name ________________________________________ Date __________________ Class __________________
UNIT
6
Exponential Relationships
Practice Test
17. The drama club had a car wash as a
fundraiser. Members washed and total of
11 vehicles charging cars $5 each and
trucks $8 each. They made $250. Find the
number of each type of vehicle they
washed during the car wash using a
systems of equations.
15. Ben has $100 in his savings account. He
is looking at two investment plans. Under
Plan A, he will increase his account
balance by $20 a year. Under Plan B, he
will increase his account balance by 15%
each year. Approximately how much will
Ben save after 3 years with each plan?
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________________________________________
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19. Travis has $60 in dimes and quarters. If
he could switch the numbers of dimes
with the number of quarters, he would
have $87. How many of each coin does
Travis have using a systems of
equations?
16. Ashley is deciding between two jobs.
Job A pays $2000 per month with a
monthly raise of $85. Job B pays $2000
per month with a monthly raise of 4%.
a. Write a function to represent the
monthly salary for Job A.
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b. Write a function to represent the
monthly salary for Job B.
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c. After how many months would Ashley
have a greater salary at Job B?
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20. Lewis checked the balance of his savings
account every month for 4 months. The
balances were $300, $410, $520, and $630.
Would a linear or exponential function better
represent the data? Explain.
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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