AnswersSummer 2026 Common Core Algebra I - MA3109 B-IC MEF22QXVExponential Decay Functions

Exponential Decay Functions — Unit test Answers

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Which graph represents a geometric sequence?

A
On a coordinate plane, 5 points are plotted. The points are (1, 1), (2, 3), (3, 5), (4, 7), (5, 9).
Option A
B
On a coordinate plane, 4 points are plotted. The points are (1, 1), (2, 2), (3, 4), (4, 8).
Option B
C
On a coordinate plane, 3 points are plotted. The points are (1, 2), (4, 4), (9, 6).
Option C
D
On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 4), (3, 9).
Option D
2
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A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2.

A
One-half
Option A
B
2
C
6
D
12
3

Select two options.

A
The graph will show exponential growth.
B
The graph will appear linear.
C
The domain will be the set of natural numbers.
D
The range will be the set of natural numbers.
E
The graph will show exponential decay.
4

Sebastian writes the recursive formula f(x+1) = 4f(x) to represent a geometric sequence whose second term is 12.

A
f(x) = 12(4)x
B
f(x) = 3(4)x − 1
C
f(x) = 4(12)x
D
f(x) = 4(3)x − 1
5

A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. Which explicit function represents the geometric sequence of the heights of the toy?

A
f(x) = 48
Option A
B
f(x) = 48
Option B
C
f(x) = 64
Option C
D
f(x) = 64
Option D
6

The points shown on the graph represent the numbers in a geometric sequence.

Question illustration
A
1
B
2
C
3
D
8
7

Which formula can be used to describe the sequence?, −4, −24, −144,...

Question illustration
A
f(x) = 6
Option A
B
f(x) = −6
Option B
C
f(x) = (6)x − 1
Option C
D
f(x) = (−6)x − 1
Option D
8

Negative 2 and two-thirds, negative 5 and one-third, negative 10 and two-thirds, negative 21 and one-third, negative 42 and two-thirds, ellipsis

Question illustration
A
f(x + 1) = –2f(x)
B
f(x + 1) = f(x)
Option B
C
f(x + 1) = f(x)
Option C
D
f(x + 1) = 2f(x)
9

A conservationist determines that a particular beach is eroding at a rate of 1.1% each year. When writing an explicit formula to represent the amount of beach remaining each year, which value should she use as the common ratio?

A
0.011
B
0.089
C
0.989
D
1.011
10

Natalia is writing a recursive formula to represent the sequence.8, 12, 18, 27, ...What value should she use as the common ratio in the formula?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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