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Exponential Growth Functions Answers

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An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made, which graph can be used to determine approximately how many years will it take for the balance to be $282?

A
Option
B
Option
C
Option
D
Option
2
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On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and curves up and increases in quadrant 1.

Question illustration
A
The domain includes all integers, and the range is y ≥ 0.
B
The domain includes all integers, and the range is y > 0.
C
The domain includes all real numbers, and the range is y ≥ 0.
D
The domain includes all real numbers, and the range is y > 0.
3

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.
4

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
5

A 2-column table has 5 rows. The first column is labeled x with entries negative 1, 0, 1, 2, 3. The second column is labeled y with entries one-tenth, one-half, five-halves, StartFraction 25 Over 2 EndFraction, StartFraction 125 Over 2 EndFraction

Question illustration
A
Twelve-fifths
Option A
B
5
C
StartFraction 25 Over 2 EndFraction
Option C
D
25
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

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
8

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.

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.
9

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.
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.
11

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
12

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
13

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
14

A collector’s item is purchased for $150 and its value increases by 3% each year. Which graph can be used to determine approximately how many years it will take for the value to double?

A
Option
B
Option
C
Option
D
Option

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