AnswersAlgebra IExponential Growth Functions

Exponential Growth Functions — Quiz Answers

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1
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Which is the graph of f of x is equal to 5 times 2 to the x th power ?

A
Image with description A coordinate plane with a curve with a positive and increasing slope. The x-axis is labeled from negative 4 to 6 in increments of 1 and the y-axis is labeled from 0 to above 40 in increments of 20. The curve begins at the left side of the plane near negative 4 comma 0, rises gradually, passes through the marked and labeled point 0 comma 5, then continues upward with an increasing slope, passing through the marked and labeled point 2 comma 10, and continues toward the upper right of the plane.
B
Image with description A coordinate plane with a curve with a positive and increasing slope. The x-axis is labeled from negative 4 to 6 in increments of 1 and the y-axis is labeled from 0 to above 40 in increments of 20. The curve begins near the lower portion of the plane, passes through the marked and labeled point 0 comma 2, then rises very steeply, passing through the marked and labeled point 2 comma 50, and continues toward the upper portion of the plane.
C
Image with description A coordinate plane with a curve with a positive and increasing slope. The x-axis is labeled from negative 4 to 6 in increments of 1 and the y-axis is labeled from 0 to above 40 in increments of 20. The curve begins near the lower left of the plane, passes through the marked and labeled point 0 comma 2, rises with an increasing slope, passes through the marked and labeled point 2 comma 10, and continues steeply toward the upper right of the plane.
D
Image with description A coordinate plane with a curve with a positive and increasing slope. The x-axis is labeled from negative 4 to 6 in increments of 1 and the y-axis is labeled from negative 20 to above 40 in increments of 20. The curve begins at the lower left near negative 4 comma 0, rises gradually, passes through the marked and labeled point 0 comma 5, then continues upward more steeply, passing through the marked and labeled point 2 comma 20, and continues toward the upper right of the plane.
2
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An account is opened with 7,595 point 9 6 dollars with a rate of increase of 2 percent per year. After 1 year, the bank account contains 7,746 point 9 0 dollars Assuming no deposits or withdrawals are made, which equation can be used to find y , the amount of money in the account after x years? (Round money values to the nearest penny.)

A
y is equal to 7,595 point 9 6 times 1 point 0 2 to the x th power
B
y is equal to 7,746 point 9 0 times 0 point 0 2 to the x th power
C
y is equal to 7,595 point 9 6 times 0 point 0 2 to the x th power
D
y is equal to 7,746 point 9 0 times 1 point 0 2 to the x th power
3

A limited-edition poster increases in value each year with an initial value of 18 dollars After 1 year and an increase of 15 percent per year, the poster is worth 20 point 7 0 dollars Which equation can be used to find the value, y , after x years? (Round money values to the nearest penny.)

A
y is equal to 20 point 7 times 0 point 1 5 to the x th power
B
y is equal to 18 times 0 point 1 5 to the x th power
C
y is equal to 18 times 1 point 1 5 to the x th power
D
y is equal to 20 point 7 times 1 point 1 5 to the x th power
4

Ramon is graphing the function f of x is equal to 3 times 4 to the x th power He begins by plotting the initial value. Which graph represents his initial step?

A
Image with description A coordinate plane with a single marked point. The x-axis is labeled from negative 5 to 5 in increments of 1. The y-axis is labeled from negative 3 to 8 in increments of 1. A point is marked and labeled 4 comma 0 on the x-axis.
B
Image with description A coordinate plane with a single marked point. The x-axis is labeled from negative 5 to 5 in increments of 1. The y-axis is labeled from negative 3 to 8 in increments of 1. A point is marked and labeled 0 comma 3 on the y-axis.
C
Image with description A coordinate plane with a single marked point. The x-axis is labeled from negative 5 to 5 in increments of 1. The y-axis is labeled from negative 3 to 8 in increments of 1. A point is marked and labeled 0 comma 4 on the y-axis.
D
Image with description A coordinate plane with a single marked point. The x-axis is labeled from negative 5 to 5 in increments of 1. The y-axis is labeled from negative 3 to 8 in increments of 1. A point is marked and labeled 3 comma 0 on the x-axis.
5

Which best describes the graph of the function f of x is equal to 4 times 1 point 5 to the x th power ?

A
The graph passes through the point 0 comma 4 , and for each increase of 1 in the x -values, the y -values increase by 1 point 5 .
B
The graph passes through the point 0 comma 1 point 5 , and for each increase of 1 in the x -values, the y -values increase by 4 .
C
The graph passes through the point 0 comma 1 point 5 , and for each increase of 1 in the x -values, the y -values increase by a factor of 4 .
D
The graph passes through the point 0 comma 4 , and for each increase of 1 in the x -values, the y -values increase by a factor of 1 point 5 .
6

After years of maintaining a steady population of 32,000 , the population of a town begins to grow exponentially. After 1 year and an increase of 8 percent per year, the population is 34,560 Which equation can be used to predict, y , the number of people living in the town after x years? (Round population values to the nearest whole number.)

A
y is equal to 34,560 times 0 point 0 8 to the x th power
B
y is equal to 34,560 times 1 point 0 8 to the x th power
C
y is equal to 32,000 times 1 point 0 8 to the x th power
D
y is equal to 32,000 times 0 point 0 8 to the x th power
7

Which is the graph of f of x is equal to 0 point 5 times 4 to the x th power ?

A
Image with description A coordinate plane with an exponential curve. The horizontal axis is labeled from negative 4 to 6 in increments of 1 and the vertical axis is labeled from 0 to 80 in increments of 16. The curve passes through the labeled points 2 comma 8, 3 comma 32, rises steeply into the first quadrant, and extends toward the left approaching the horizontal axis without touching it.
B
Image with description A coordinate plane with an exponential curve. The horizontal axis is labeled from negative 4 to 6 in increments of 1 and the vertical axis is labeled from 0 to 80 in increments of 16. The curve passes through the labeled points 3 comma 8, 4 comma 16, and rises steeply into the first quadrant, and extends toward the left approaching the horizontal axis without touching it.
C
Image with description A coordinate plane with an exponential curve. The horizontal axis is labeled from negative 4 to 6 in increments of 1 and the vertical axis is labeled from 0 to 80 in increments of 16. The curve passes through the labeled points 1 comma 8, 3 comma 32, and rises steeply into the first quadrant, extending toward the left approaching the horizontal axis without touching it.
D
Image with description A coordinate plane with an exponential curve. The horizontal axis is labeled from negative 4 to 6 in increments of 1 and the vertical axis is labeled from 0 to 80 in increments of 16. The curve passes through the labeled points 1 comma 8, 2 comma 16, and 2 comma 64, rises steeply into the first quadrant, and extends toward the left approaching the horizontal axis without touching it.
8

A function of the form f of x is equal to A b to the x th power is modified so that the b value remains the same but the a value is increased by 2 How do the domain and range of the new function compare to the domain and range of the original function? Choose two correct answers.

A
The range becomes y is greater than or equal to 2 .
B
The range stays the same.
C
The domain becomes x is greater than or equal to 2 .
D
The domain stays the same.
E
The range becomes y is greater than 2 .
F
The domain becomes x is greater than 2 .
9

Josiah invests 360 dollars into an account that accrues 3 percent interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah’s account, y , after x years?

A
y is equal to 360 times 1 point 3 to the x th power
B
y is equal to 360 times 0 point 0 3 to the x th power
C
y is equal to 360 times 1 point 0 3 to the x th power
D
y is equal to 360 times 0 point 3 to the x th power
10

Which graph shows exponential growth?

A
Image with description A coordinate plane with both the axis labeled from negative 5 to 5. A straight line with positive slope crosses the y-axis at negative 1 comma 0 and crosses the y-axis at 2 comma 0.
B
Image with description A coordinate plane with both the axis labeled from negative 5 to 5. A curve approaches y equals 0 in quadrant 2 and curves up into quadrant 1. The y-intecept is 0 comma 2.
C
Image with description A coordinate plane with both the axis labeled from negative 5 to 5. A parabola opens upwards with vertex at 0 comma 0. The curve also crosses the points negative 1 comma 2 and 1 comma 2.
D
Image with description A coordinate plane with both the axis labeled from negative 5 to 5. A curve opens down and to the right in quadrants 1 and 4. It crosses the x-axis at 1 comma 0. It also touches the negative y-axis at 0 comma 2, 0 comma 3, and 0 comma 4.

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