AnswersCommon Core Algebra I B-ICExponential Growth Functions

Exponential Growth Functions Answers

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1
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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
2
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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
3

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
4

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
5

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
6

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
7

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.
8

A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)

A
y = 18(1.15)x
B
y = 18(0.15)x
C
y = 20.7(1.15)x
D
y = 20.7(0.15)x
9

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
10

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.

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