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

Exponential Decay Functions — Cumulative exam Answers

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The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?

A
The depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm.
B
The depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour.
C
The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.
D
The depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour.
2
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y = 5x + 23x = –y + 10

A
(–4, –18)
B
(–18, –4)
C
(7, 1)
D
(1, 7)
3

On a coordinate plane, solid circles appear at the following points: (negative 5, negative 3), (negative 4, negative 4), (negative 2, 2), (1, 3), (1, negative 2), (2, 1), (5, negative 4).

Question illustration
A
(–2, 2)
B
(1, 3)
C
(5, –4)
D
(–4, –4)
4

The function f(x) is shown on the graph.

Question illustration
A
0 only
B
–6 only
C
–2, 1, or 3 only
D
–6, –2, 1, or 3 only
5

The function f(x) is shown on the graph.

Question illustration
A
0 only
B
–6 only
C
–2, –1, 1, and 3 only
D
–6, –2, –1, 1, and 3 only
6

A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?

A
y = –3x
B
y = –
Option B
C
y =
Option C
D
y = 3x
7

Which is the initial value that shrinks an exponential growth function by 50%?

A
One-fifth
Option A
B
One-fourth
Option B
C
One-third
Option C
D
One-half
Option D
8

2x + 4y = 12y = x – 3

Question illustration
A
(–1, 8)
B
(8, –1)
C
(5, StartFraction one-half EndFraction)
Option C
D
(StartFraction one-half EndFraction, 5)
Option D
9

The axis of symmetry for a quadratic equation can be found using the formula , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane.What is the equation when solved for a?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

The table represents a linear equation.

Question illustration
A
y – 6 = (x – 2)
Option A
B
y – 6 = (x – 2)
Option B
C
y + 6 = (x + 2)
Option C
D
y + 6 = (x + 2)
Option D
11

Lukas graphed the system of equations shown.2x + 3y = 2y = x + 3What is the solution to the system of equations?

Question illustration
A
(–2, 2)
B
(0, 0.67)
C
(0, 3)
D
(1, 0)
12

Consider the function represented by the graph.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
13

A frozen yogurt shop offers a rewards system for frequent customers. The graph below represents how much a rewards customer pays based on the number of ounces of frozen yogurt purchased.

Question illustration
A
A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.
B
A rewards customer pays $5 per ounce because the total amount paid is always increasing.
C
A rewards customer pays $20 for 10 or 12 ounces of yogurt because the total amount paid is increasing.
D
A rewards customer earns 5 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.
14

Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

Question illustration
A
v +4 = 8 – v
Option A
B
v +4 = 8
Option B
C
4 + v = 8 – v
Option C
D
2v + 4 = 8
15

The table represents a linear function.

Question illustration
A
–10
B
–5
C
5
D
10
16

Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?

A
(x + 30 + 60) = x
Option A
B
(x) = x(30 + 60)
Option B
C
x(30 + 60) = x
Option C
D
(x) = (30 + 60)
Option D
17

The price of grapes at the grocery store is $1.44 per pound. There are approximately 0.45 kilograms in a pound. To the nearest cent, what is the price of grapes in dollars per kilogram?

A
$0.65 per kilogram
B
$0.99 per kilogram
C
$1.89 per kilogram
D
$3.20 per kilogram
19

On a coordinate plane, a red line, labeled g of x, begins on a negative slope, crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and crosses the x-axis on a positive slope at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 2) and the x-axis at (2, 0).

Question illustration
A
f(2) = g(2)
B
f(0) = g(0)
C
f(2) = g(0)
D
f(0) = g(2)
20

How many solutions exist for the given equation?3(x + 10) + 6 = 3(x + 12)

A
zero
B
one
C
two
D
infinitely many
21

Consider the function represented by the equation x – y = 3. What is the equation written in function notation, with x as the independent variable?

A
f(x) = y + 3
B
f(x) = –y – 3
C
f(x) = –x + 3
D
f(x) = x – 3

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