AnswersAlgebra IExponential Decay Functions

Exponential Decay Functions — Quiz Answers

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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 range is y is greater than 0 .
B
The range is the set of all real numbers.
C
The domain is x is greater than 0 .
D
The domain 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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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 0 point 8 5 to the x th power
B
f of x is equal to 20,000 times 1 point 8 5 to the x th power
C
f of x is equal to 20,000 times 0 point 1 5 to the x th power
D
f of x is equal to 20,000 times 1 point 1 5 to the x th power
3

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

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 0 3 to the x th power
B
f of x is equal to 1 comma 200 times 1 point 0 3 to the x th power
C
f of x is equal to 1 comma 200 times 0 point 9 7 x
D
f of x is equal to 1 comma 200 times 0 point 9 7 to the x th power
5

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 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).
B
Image with description 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).
C
Image with description 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).
D
Image with description 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).
6

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 On a coordinate plane, the point (0, 0.25) is graphed.
B
Image with description On a coordinate plane, the point (0, 20) is graphed.
C
Image with description On a coordinate plane, the point (20, 0) is graphed.
D
Image with description On a coordinate plane, the point (0.25, 0) is graphed.
7

Which graph represents exponential decay?

A
Image with description On a coordinate plane, a graph starts at negative 2 comma 0 and curves up and to the right into quadrant 1. The curve intersects y-axis at 0 comma between 4 and 5.
B
Image with description On a coordinate plane, a graph approaches y is equal to 0 in quadrant 1 and curves up into quadrant 2. The curve intersects y-axis at 0 comma 1.
C
Image with description On a coordinate plane, a straight line has a negative slope. The line intersects y-axis at 0 comma 1 and x-axis at between 0 and 1 comma 0.
D
Image with description On a coordinate plane, a graph approaches y is equal to 0 in quadrant 2 and curves up into quadrant 1. The curve intersect y-axis at 0 comma 1.
8

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 0 point 4 to the x th power , with a horizontal asymptote of y is equal to 0
C
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
D
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
9

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
0 point 4
B
1 point 5
C
0 point 6
D
2 point 5
10

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

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Exponential Decay Functions — Quiz Answers —…