AnswersCommon Core Algebra I B-ICExponential Growth Functions

Exponential Growth Functions Answers

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1
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Which graph shows exponential growth?

A
On a coordinate plane, a parabola opens up with vertex at (0, 0).
Option A
B
On a coordinate plane, a curve approaches y = 0 in quadrant 2 and curves up into quadrant 1.
Option B
C
On a coordinate plane, a straight line with positive slope crosses the y-axis at (negative 1, 0) and crosses the y-axis at (2, 0).
Option C
D
On a coordinate plane a curve opens down and to the right in quadrants 1 and 4. It crosses the x-axis at (1, 0).
Option D
2
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Which best describes the graph of the function f(x) = 4(1.5)x?

A
The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by 1.5.
B
The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5.
C
The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by 4.
D
The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by a factor of 4.
3

Which equation represents an exponential function that passes through the point (2, 36)?

A
f(x) = 4(3)x
B
f(x) = 4(x)3
C
f(x) = 6(3)x
D
f(x) = 6(x)3
4

A function of the form f(x) = abx 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? Check all that apply.The range stays the same. The range becomes y > 2.The domain stays the same. The domain becomes x > 2.The range becomes y ≥ 2.The domain becomes x ≥ 2.

A
The range stays the same.
B
The range becomes y > 2.
C
The domain stays the same.
D
The domain becomes x > 2.
E
The range becomes y ≥ 2.
F
The domain becomes x ≥ 2.
5

Which equation represents an exponential function that passes through the point (2, 80)?

A
f(x) = 4(x)5
B
f(x) = 5(x)4
C
f(x) = 4(5)x
D
f(x) = 5(4)x
6

How would the graph change if the b value in the equation is decreased but remains greater than 1? Check all that apply.

A
The graph will begin at a lower point on the y-axis.
B
The graph will increase at a faster rate.
C
The graph will increase at a slower rate.
D
The y-values will continue to increase as x-increases.
E
The y-values will each be less than their corresponding x-values.
7

Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x. She makes these two statements:1. As x increases infinitely, the y-values are continually doubled for each single increase in x.2. As x decreases infinitely, the y-values are continually halved for each single decrease in x.

A
Statement 1 is incorrect because the y-values are increased by 2, not doubled.
B
Statement 2 is incorrect because the y-values are doubled, not halved.
C
The conclusion is incorrect because the range is limited to the set of integers.
D
The conclusion is incorrect because the range is limited to the set of positive real numbers.
8

Josiah invests $360 into an account that accrues 3% 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 = 360(1.3)x
B
y = 360(0.3)x
C
y = 360(0.03)x
D
y = 360(1.03)x
9

Which is the graph of f(x) = 5(2)x?

A
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 5) and (2, 20).
Option A
B
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 2) and (2, 50).
Option B
C
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 2) and (2, 10).
Option C
D
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 5) and (2, 10).
Option D
10

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% 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 = 32,000(1.08)x
B
y = 32,000(0.08)x
C
y = 34,560(1.08)x
D
y = 34,560(0.08)x

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