AnswersSummer 2026 Common Core Algebra I - MA3109 B-IC MEF22QXVExponential Decay Functions

Exponential Decay Functions Answers

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Chelsea is graphing the function f(x) = 20()x. She begins by plotting the initial value. Which graph represents her first step?

Question illustration
A
On a coordinate plane, the point (0, 0.25) is graphed.
Option A
B
On a coordinate plane, the point (0.25, 0) is graphed.
Option B
C
On a coordinate plane, the point (0, 20) is graphed.
Option C
D
On a coordinate plane, the point (20, 0) is graphed.
Option D
2
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The graph of f(x) = 2x is shown on the grid.

Question illustration
A
On a coordinate plane, an exponential function approaches x = 0 in quadrant 4 and increases into quadrant 1.
Option A
B
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0.
Option B
C
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and curves down into quadrant 4.
Option C
D
On a coordinate plane, an exponential function approaches x = 0 in quadrant 1 and curves down and to the right into quadrant 4.
Option D
3

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Answer not available
4

Which is the graph of ?

Question illustration
A
Option
B
Option
C
Option
D
Option
5

What is the multiplicative rate of change for the exponential function f(x) = ?

Question illustration
A
0.4
B
0.6
C
1.5
D
2.5
6

Which is the graph of f(x) = 100(0.7)x?

A
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).
Option A
B
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 9) and (0, 100).
Option B
C
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 70) and (0, 100).
Option C
D
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 30) and (0, 100).
Option D
7

The table represents an exponential function.

Question illustration
A
0.2
B
0.25
C
0.5
D
0.75
8

Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value?

A
f(x) = 20,000(0.85)x
B
f(x) = 20,000(0.15)x
C
f(x) = 20,000(1.15)x
D
f(x) = 20,000(1.85)x
9

The table represents an exponential function.

Question illustration
A
One-third
Option A
B
Two-thirds
Option B
C
2
D
9
10

Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. What multiplicative rate of change should Hal use in his function?

A
0.02
B
0.98
C
1.02
D
1.98

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