1. Exponential Equations
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550
Exponential Equations
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2. $550 c A new car that sells for $44,000
depreciates 25% each year. Write the
equation that models the value of
the car.
y= (1.25)x
y= 44000−(0.75)x
y= 44000(0.75)x
y= 0.75 (44000)x
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ANSWER c
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3. $800
The bear population in a given area is increasing at a rate of 2% per year. The population is currently about If this trend continues what it is predicted population after 8 years? Round to the nearest whole number.
1344
6793.7
1744
1851
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ANSWER
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4. $500 a Which exponential function is shown in the graph? y= ( 𝟏 𝟑 )x
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ANSWER a
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5. $300 b Which functions model Exponential decay? y= 0.5 (5)x
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ANSWER b
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6. $500 b y= 5(2)x y= 5 (0.5)x y= 5x y= 0.5 (5)x
The table below contains some points on the graph of an exponential function.
Based on the table, which function represents the same relationship?
y= 5(2)x
y= 5 (0.5)x
y= 5x
y= 0.5 (5)x x y -2 20 -1 10 5 1
2.5
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ANSWER

7. $600 a y= 6(5)x y= 5(6)x y= 6x y= 3(5)x
The table below contains some points on the graph of an exponential function.
Based on the table, which function represents the same relationship?
y= 6(5)x
y= 5(6)x
y= 6x
y= 3(5)x x y -2
0.24 -1
1.2 6 1 30
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ANSWER

8. $5000
Joana is hiring her son to point the garage. She has given him two options of paying him. She estimate the job will take 8 hours and she will pay him when the job is completed. Which option is the best?
Option A: $15 per hours.
Option B: First 3 hour 3$ and then she will double this for each hour until the job is done.
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Option b
ANSWER
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9. $600
An investment of $65,000 is increasing a rate of 3.2% per year. The investment continues at this rate for 8 years. Find the value of the investment after 8 years.
83628
599108
50109
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ANSWER
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10. $300 b Which functions model exponential decay? y= 0.5 ( 𝟓 𝟐 )x
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ANSWER
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11. $700 a Which exponential function is shown in the graph?
y= 10 ( 𝟏 𝟐 )x
y= -2 (10)x
y= -10( 𝟏 𝟐 )x
y= 10 (2)x
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ANSWER a
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12. $450
A new phone valued at $650 depreciates at a rate of 34.3% per year.
What is the value of the computer after 3 years?
970 64
26.23
184
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ANSWER
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13. $350 c Which exponential function is shown in the graph? y= ( 𝟏 𝟐 )x
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ANSWER c
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14. $800
If the number of bacteria in a colony doubles every 13 hours and there is currently a population of 100,000 bacteria, what will the population be 26 hours from now?
400,000
2,600,000
1,300,000
800,000
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ANSWER a
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15. $300
The table below contains some points on the graph of an exponential function.
Based on the table, which function represents the same relationship? x y -2
230.4 -1
76.8
25.6 1
8.53
y= 8.53(3)x
y= 8.53 ( 𝟏 𝟑 )x
y= 25.6 ( 𝟏 𝟑 )x
y= 𝟏 𝟑 (25.6)x
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ANSWER
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16. $400 a Which exponential function is shown in the graph?
y= 100 ( 𝟏 𝟐 )x
y= 𝟏 𝟐 (100)x
y= 100 ( 𝟏 𝟑 )x
y= 𝟏 𝟑 (𝟏𝟎𝟎)x
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ANSWER a
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17. $600
Each year the local country club sponsor a tennis tournament. Play starts with 128 participant. During each round, half of the players are eliminated. How many players remain after 5 round? 4 2 6 8
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ANSWER

18. $900 b y= 6191 (0.4)x y= 6191(1.04)x y= 6191 (1.4)x y= 6191(0.04)x
The population of Winnemucca, Nevada was in 1990 and started increasing at a rate of 4% each year. What is the equation that can model the population for the following years?
y= 6191 (0.4)x
y= 6191(1.04)x
y= 6191 (1.4)x
y= 6191(0.04)x b
ANSWER
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19. $300
What graph shows exponential growth?
A) B) C)
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ANSWER B
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20. $500
The table below contains some points on the graph of an exponential function.
Based on the table, which function represents the same relationship?
y= 5(2)x
y= 5 (5)x
y= 2x
y= 5x x y 1 5 2 25 3
125
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ANSWER

21. $900 a y= 500(0.96)x y= 500(1.04)x y= 500(0.4)x y= 500(0.04)x
A 500 mL puddle of water is evaporating at a rate of 4% per hour. Write a function that represents the amount of water in the puddle at a given time. Use x for hours and y for the amount of water left in the puddle.
y= 500(0.96)x
y= 500(1.04)x
y= 500(0.4)x
y= 500(0.04)x a
ANSWER
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22. $300 d Given the equation y = 1.4(1.03)x What statement is true?
The graph shows exponential decay and the rate of decay is 1.4
The graph shows exponential growth and the rate of growth is 1.4
The graph shows exponential decay and the rate of decay is 1.03
The graph shows exponential growth and the rate of growth is 1.03
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ANSWER d

23. $400 b Given the equation y = 𝟏 𝟐 (5)x What statement is true?
The graph shows exponential decay and the rate of decay is 𝟏 𝟐
The graph shows exponential growth and the rate of growth is 5
The graph shows exponential decay and the rate of decay is 5
The graph shows exponential growth and the rate of growth is 𝟏 𝟐
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ANSWER b

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