AnswersCA-Mathematics IExponential Growth Functions

Exponential Growth Functions Answers

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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
2
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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
3

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
4

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
5

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
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% 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
7

On a coordinate plane, an exponential growth function approaches y = 0 in the second quadrant and goes through points (negative 1, 0.8), (0, 2), (1, 5), (2, 12.5).

Question illustration
A
2.00
B
2.50
C
5.25
D
10.50
8

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
9

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
10

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
11

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.
12

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

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