AnswersAISD Algebraic Reasoning A Credit Recovery 2026-2027Modeling Functions Using Finite Differences

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 statements could he include in his explanation? Select two options.

A
The domain of both functions is all real numbers.
B
The domain of f(x) is x > 5.
C
The domain of g(x) is x > 5.
D
The range of f(x) is y > 0.
E
The range of g(x) is y > 0.
4

Several ordered pairs from a continuous exponential function are shown in the table.

Question illustration
A
The domain is the set of integers, and the range is y > 4.
B
The domain is the set of integers, and the range is y > 0.
C
The domain is the set of real numbers, and the range is y > 0.
D
The domain is the set of real numbers, and the range is y > 4.
5

Which is the graph of f(x) = 0.5(4)x?

A
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 1), (2, 8), (3, 32).
Option A
B
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 4), (1, 16), (2, 64).
Option B
C
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 1), (3, 8), (4, 16).
Option C
D
On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (0, 1), (1, 8), (2, 32).
Option D
6

Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?

A
On a coordinate plane, the point (0, 3) is graphed.
Option A
B
On a coordinate plane, the point (0, 4) is graphed.
Option B
C
On a coordinate plane, the point (3, 0) is graphed.
Option C
D
On a coordinate plane, the point (4, 0) is graphed.
Option D
7

The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500 and its value increases at a rate of 5% per year. Find the value of the item after 4 years.

A
$578.81
B
$607.75
C
$1687.50
D
$2531.25
8

A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation?

A
y = 1,000(1.15)6; 2,313 bacteria
B
y = 1,000(1.15)7; 2,660 bacteria
C
y = 1,000(1.5)5; 7,594 bacteria
D
y = 1,000(1.5)6; 11,391 bacteria
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

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.

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