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

Exponential Decay Functions Answers

0 verified answers1 views
1
Free Preview

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
Free Preview

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
3

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
4

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
5

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).
6

Which graph represents exponential decay?

A
On a coordinate plane, a straight line has a negative slope.
Option A
B
On a coordinate plane, a graph starts at (negative 2, 0) and curves up and to the right into quadrant 1.
Option B
C
On a coordinate plane, a graph approaches y = 0 in quadrant 1 and curves up into quadrant 2.
Option C
D
On a coordinate plane, a graph approaches y = 0 in quadrant 2 and curves up into quadrant 1.
Option D
7

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
8

Which are true of the function f(x) = 49? Select three options.

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.
9

The table represents an exponential function.

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

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)

Did you find these answers helpful?

More from this Course

Quiz
10 verified answers

Vertical Stretches and Shrinks of Exponential Functions

Quiz
10 verified answers

Exponential Functions with Radical Bases

Quiz
10 verified answers

Exponential Decay Functions