AnswersMathematics for College Liberal Arts Sem 1 1207350 BCPS 2025-26Unit Test

Introduction to Modeling with Functions Answers

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1
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The graph shows the daily revenue earned selling coupon cards in a fundraiser if the price is decreased by x dollars.

Question illustration
A
R(x) = –x2 + 6x + 40
B
R(x) = –(x – 4)(x + 10)
C
R(x) = –(x2 – 14x + 40)
D
R(x) = –(x + 3)2 + 49
2
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The graph represents the expected hourly revenue, in dollars, y, earned by a car wash for each decrease of x dollars in the price of a car wash.

Question illustration
A
$100
B
$150
C
$200
D
$225
3

The speed of a falling object increases at a constant rate as time increases since the object was dropped. Which graph could represent the relationship between t, time in seconds, and s, speed in meters per second?

Question illustration
A
A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line increases from 0 to 10 seconds.
Option A
B
A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line decreases from 0 to 4 seconds.
Option B
C
A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line increases from 0 to 4.5 seconds.
Option C
D
A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line decreases from 1 to 9 seconds.
Option D
4

The graph shows the population of a bacteria in an experiment, measured every hour.

Question illustration
A
f(t) = 10(1.4)t
B
f(t) = 10(2.0)t
C
f(t) = 14(1.4)t
D
f(t) = 14(2.0)t
5

Which statements are true about the relationship between the depth of the snow and the height of water in the jar after the snow is melted? Select two options.

A
The points on a graph representing the relationship lie on a line.
B
There is 0.4 inch of water to every 1 inch of snow.
C
A line through the points will pass through (0, 0).
D
The function relating snow depth to water depth is quadratic.
E
The data can be represented by f(x) = 0.2x.
6

Sophia plots points on a graph to represent the shape of a concave lens.

Question illustration
A
linear
B
exponential
C
quadratic
D
square root
7

A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic.Which graph could represent the area of each rectangle in terms of the change in the length and width?

Question illustration
A
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A straight line decreases from 0 to 9 units.
Option A
B
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line decreases from 0 to 3 units, increases from 3 to 6 seconds, and decreases from 6 to 9 seconds.
Option B
C
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
Option C
D
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A curved line decreases from 0 to 9 units.
Option D
8

A graph is drawn to represent a relationship between distance, d, and time, t.

Question illustration
A
Each point shows the distance, in feet, above the ground of a falling object after t seconds, where the falling speed increases as time increases.
B
Each point shows the distance, in feet, covered t seconds after a brake is applied, where the speed of the car decreases by a constant factor.
C
Each point shows the distance, in feet, traveled by an airplane on a runway by gradually increasing speed t seconds after being approved for takeoff.
D
Each point shows the remaining distance, in feet, to the finish line of a race t seconds after a runner begins the final stretch and runs at a constant speed.
9

The half life of a certain substance is about 4 hours. The graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours.

Question illustration
A
y = 25(0.15)t
B
y = 25(0.85)t
C
y = 50(0.15)t
D
y = 50(0.85)t
10

The speed of a falling object increases at a constant rate as time increases since the object was dropped. Which graph could represent the relationship between t, time in seconds, and s, speed in meters per second?

A
A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line increases from 0 to 10 seconds.
Option A
B
A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line decreases from 0 to 4 seconds.
Option B
C
A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line increases from 0 to 4.5 seconds.
Option C
D
A graph shows dropping time (seconds) labeled 1 to 10 on the horizontal axis and object speed (meters per second) on the vertical axis. A line decreases from 1 to 9 seconds.
Option D
11

A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic.Which graph could represent the area of each rectangle in terms of the change in the length and width?

A
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A straight line decreases from 0 to 9 units.
Option A
B
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line decreases from 0 to 3 units, increases from 3 to 6 seconds, and decreases from 6 to 9 seconds.
Option B
C
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
Option C
D
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A curved line decreases from 0 to 9 units.
Option D
12

The graph shows the relationship between a gift card balance and the number of visits to a smoothie shop.

Question illustration
A
$18.00
B
$4.00
C
$3.00
D
$6.00
13

Brandon enters a contest at the gym. He earns 1 point for his first workout. If he works out the next day, he earns double the points of the previous day. Brandon creates the graph to show the number of points that can be earned on the nth consecutive day of working out.

Question illustration
A
8
B
32
C
64
D
128
14

Cherie measures and records the lengths and sizes of the same style of a sandal found at a shoe store.

Question illustration
A
S = x – 2
B
S = 2x – 10
C
S = x + 6
D
S = 2x + 4
15

The graph shows the distance, in feet, required for a car to come to a full stop if the brake is fully applied and the car was initially traveling x miles per hour.

Question illustration
A
y =
Option A
B
y =
Option B
C
y =
Option C
D
y =
Option D
16

The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. Iron has a half-life of 2.7 years. Which equation gives the mass of a 200 mg iron sample remaining after t years, and approximately how many milligrams remain after 12 years?

Question illustration
A
; 2.6 mg
Option A
B
f(t)=2.7(0.5)t; 0.0007 mg
C
f(t)=200(0.5)t; 0.05 mg
D
; 9.2 mg
Option D
17

A graph is drawn to represent a relationship between distance, d, and time, t.

Question illustration
A
Each point shows the distance, in feet, above the ground of a falling object after t seconds, where the falling speed increases as time increases.
B
Each point shows the distance, in feet, covered t seconds after a brake is applied, where the speed of the car decreases by a constant factor.
C
Each point shows the distance, in feet, traveled by an airplane on a runway by gradually increasing speed t seconds after being approved for takeoff.
D
Each point shows the remaining distance, in feet, to the finish line of a race t seconds after a runner begins the final stretch and runs at a constant speed.
18

The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?

Question illustration
A
; 13.5 mg
Option A
B
; 34.6 mg
Option B
C
; 0.2 mg
Option C
D
; 4.6 mg
Option D
19

Lindsay is creating a bridge out of dried pasta and glue. In her plans, she sketches the graph to determine the lengths of the noodles, in centimeters, needed for the arch to increase the length of the bridge in 1-centimeter increments.

Question illustration
A
f(x) = (x – 5)2 + 8
B
f(x) = –(x + 5)2 + 8
C
f(x) = 0.5(x + 5)2 + 8
D
f(x) = –0.5(x – 5)2 + 8
20

The graph shows the daily revenue earned selling coupon cards in a fundraiser if the price is decreased by x dollars.

Question illustration
A
R(x) = –x2 + 6x + 40
B
R(x) = –(x – 4)(x + 10)
C
R(x) = –(x2 – 14x + 40)
D
R(x) = –(x + 3)2 + 49

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