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

Exponential Decay Functions Answers

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Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?

A
f(x) = 1,200(1.03)x
B
f(x) = 1,200(0.03)x
C
f(x) = 1,200(0.97)x
D
f(x) = 1,200(0.97x)
2
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A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, 40% of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after x days of treatment?

A
f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0
B
f(x) = 5000(0.6)x, with a vertical asymptote of x = 0
C
f(x) = 5000(1.4)x, with a horizontal asymptote of y = 0
D
f(x) = 5000(1.6)x, with a vertical asymptote of x = 0
3

Two exponential functions are shown in the table.

Question illustration
A
The functions f(x) and g(x) are reflections over the x-axis.
B
The functions f(x) and g(x) are reflections over the y-axis.
C
The function f(x) is a decreasing function, and g(x) is an increasing function.
D
The function f(x) has a greater initial value than g(x).
4

Which are true of the function f(x) = 49? Select three options.The domain is the set of all real numbers. The range is the set of all real numbers. The domain is x > 0.The range is y > 0.As x increases by 1, each y-value is one-seventh of the previous y-value.

Question illustration
A
The domain is the set of all real numbers.
B
The range is the set of all real numbers.
C
The domain is x > 0.
D
The range is y > 0.
E
As x increases by 1, each y-value is one-seventh of the previous y-value.
5

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
6

The table represents an exponential function.

Question illustration
A
One-third
Option A
B
Two-thirds
Option B
C
2
D
9
7

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
8

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
9

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
10

Which is an exponential decay function?

A
f start bracket x end bracket equals Three-fourths start bracket Seven-fourths end bracket superscript x
Option A
B
f start bracket x end bracket equals two-third start bracket Four-fifths end bracket superscript negative x
Option B
C
f start bracket x end bracket equals Three-halves start bracket Eight-sevenths end bracket superscript negative x
Option C
D
f start bracket x end bracket equals one-third start bracket negative nine-halves end bracket superscript x
Option D

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