AnswersCMS 2026-2027 NC Math 1 CREDIT RECOVERYExponential Decay Functions

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Which are true of the function f of x is equal to 49 times 1 seventh to the x th power ? Choose three correct answers.

A
The domain is the set of all real numbers.
B
The domain is x is greater than 0 .
C
The range is y is greater than 0 .
D
The range is the set of all real numbers.
E
As x increases by 1 , each y -value is one-seventh of the previous y -value.
2
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Which is an exponential decay function?

A
f of x is equal to 2 thirds times 4 fifths raised to the negative x power
B
f of x is equal to 3 fourths times 7 fourths to the x th power
C
f of x is equal to 3 halves times 8 sevenths raised to the negative x power
D
f of x is equal to 1 third times negative 9 halves to the x th power
3

Which is the graph of f of x is equal to 100 times 0 point 7 to the x th power ?

A
Image with description A coordinate plane with a curve. The horizontal axis is labeled from negative 5 to 5 in increments of 1 and the vertical axis is labeled from negative 100 to 100 in increments of 50. The curve passes through the labeled points 0 comma 100 and 2 comma 49, and descends from left to right.
B
Image with description A coordinate plane with a curve. The horizontal axis is labeled from negative 5 to 5 in increments of 1 and the vertical axis is labeled from negative 100 to 100 in increments of 50. The curve passes through the labeled points 0 comma 100 and 2 comma 30, and descends steeply from left to right.
C
Image with description A coordinate plane with a curve. The horizontal axis is labeled from negative 5 to 5 in increments of 1 and the vertical axis is labeled from negative 100 to 100 in increments of 50. The curve passes through the labeled points 0 comma 100 and 2 comma 70, and descends gradually from left to right.
D
Image with description A coordinate plane with a curve. The horizontal axis is labeled from negative 5 to 5 in increments of 1 and the vertical axis is labeled from negative 100 to 100 in increments of 50. The curve passes through the labeled points 0 comma 100 and 2 comma 70, and descends from left to right.
4

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

A
f of x is equal to 20,000 times 1 point 1 5 to the x th power
B
f of x is equal to 20,000 times 0 point 1 5 to the x th power
C
f of x is equal to 20,000 times 0 point 8 5 to the x th power
D
f of x is equal to 20,000 times 1 point 8 5 to the x th power
5

A population of bacteria is treated with an antibiotic. It is estimated that 5 comma 000 live bacteria existed in the sample before treatment. After each day of treatment, 40 percent 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 of x is equal to 5000 times 1 point 4 to the x th power , with a horizontal asymptote of y is equal to 0
B
f of x is equal to 5000 times 1 point 6 to the x th power , with a vertical asymptote of x is equal to 0
C
f of x is equal to 5000 times 0 point 4 to the x th power , with a horizontal asymptote of y is equal to 0
D
f of x is equal to 5000 times 0 point 6 to the x th power , with a vertical asymptote of x is equal to 0
6

What is the multiplicative rate of change for the exponential function f of x is equal to 2 times 5 halves raised to the negative x power ?

A
1 point 5
B
0 point 6
C
2 point 5
D
0 point 4
7

Which graph represents exponential decay?

A
Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 and a vertical y-axis labeled from negative 1 to 9 in increments of 1. The curve begins in the second quadrant near the coordinate point negative 2 comma 0 with a downward-pointing arrowhead touching the x-axis at negative 2. From this point, it curves steeply upwards and to the right, crossing through the point negative 1 comma 4 and the y-axis at 0 comma 4 point 5. It then curves more gradually into the first quadrant, passing near the point 2 comma 5 and continuing towards the right to an arrowhead pointing near 6 comma 5 point 7.
B
Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 and a vertical y-axis labeled from negative 1 to 9 in increments of 1. The curve passes through the coordinate point negative 1 comma 3, and extends upwards to negative 2 comma 9. The curve decreases sharply downwards, crossing the y-axis at 0 comma 1. It then enters the first quadrant, passing near 1 comma 0 point 3 and flattening along the x-axis.
C
Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 and a vertical y-axis labeled from negative 1 to 9 in increments of 1. The curve starts flat near the x-axis in the second quadrant with an arrowhead pointing near negative 3 point 5 comma 0. Moving from left to right, it passes through negative 1 comma 0 point 3, crosses the y-axis at 0 comma 1, and enters the first quadrant. As it moves further right, it grows steeply upwards, passing through 1 comma 3, and continuing upwards to an arrowhead pointing near 2 comma 9.
D
Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 and a vertical y-axis labeled from negative 1 to 9 in increments of 1. A linear function shown as a straight line is plotted on the grid. The line has a negative slope, passing through the y-axis at 0 comma 1 and the x-axis near 0 point 5 comma 0. It extends upwards into the second quadrant, passing through the coordinate point negative 1 comma 3, and continuing upwards to an arrowhead pointing near negative 4 comma 9. It extends downwards into the fourth quadrant with an arrowhead pointing near 1 comma negative 1.
8

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

A
1 point 0 2
B
0 point 9 8
C
0 point 0 2
D
1 point 9 8
9

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

A
f of x is equal to 1 comma 200 times 0 point 9 7 x
B
f of x is equal to 1 comma 200 times 0 point 0 3 to the x th power
C
f of x is equal to 1 comma 200 times 1 point 0 3 to the x th power
D
f of x is equal to 1 comma 200 times 0 point 9 7 to the x th power
10

Chelsea is graphing the function f of x is equal to 20 times 1 fourth to the x th power She begins by plotting the initial value. Which graph represents her first step?

A
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A point is plotted at the point 20 comma 0.
B
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A point is plotted at the point 0.25 comma 0.
C
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A point is plotted at the point 0 comma 20.
D
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A point is plotted at the point 0 comma 0.25.

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