AnswersAZ-Common Core Algebra II BIntroduction to Modeling with Functions

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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Alicia bought a notebook and several erasers at the student store. The graph shows the relationship between the total cost of her items and the number of erasers she purchased.

Question illustration
A
$1.00
B
$1.50
C
$2.00
D
$3.50
3

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
4

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.
5

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
6

The graph shows the relationship between the weight of a box and the number of books added to the box.

Question illustration
A
f(x) = 0.5x + 1.5
B
f(x) = 0.75x + 2
C
f(x) = 1.5x + 0.5
D
f(x) = 2x + 0.75
7

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
8

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
9

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
10

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
11

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
12

Julia finds that the data in the table can be modeled by the function y = 5(4)x.

Question illustration
A
Julia is correct because the distance starts at 5 feet and increases by a factor of 4.
B
Julia is correct because the function is true for (0, 5) and (1, 20).
C
Julia is not correct because the function is not true for the point (2, 80).
D
Julia is not correct because the distance does not increase by a constant factor each minute.
13

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
14

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
15

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
16

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
17

Julia finds that the data in the table can be modeled by the function y = 5(4)x.

Question illustration
A
Julia is correct because the distance starts at 5 feet and increases by a factor of 4.
B
Julia is correct because the function is true for (0, 5) and (1, 20).
C
Julia is not correct because the function is not true for the point (2, 80).
D
Julia is not correct because the distance does not increase by a constant factor each minute.

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