AnswersAlgebra Concepts and ConnectionsIntroduction to Modeling with Functions

Introduction to Modeling with Functions — Quiz Answers

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1
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How many points will Brandon earn on day 8 if he works out each of the previous 7 days?

A
32
B
128
C
8
D
64
2
Free Preview

What is the hourly revenue if there is no decrease in price?

A
200 dollars
B
100 dollars
C
150 dollars
D
225 dollars
3

Which situation could be represented on the graph?

A
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.
B
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.
C
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.
D
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.
4

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? Choose two correct answers.

A
The data can be represented by f of x is equal to 0 point 2 to the x th power .
B
There is 0 point 4 inch of water to every 1 inch of snow.
C
The points on a graph representing the relationship lie on a line.
D
A line through the points will pass through 0 comma 0 .
E
The function relating snow depth to water depth is quadratic.
5

What is the amount spent on each visit to the smoothie shop?

A
6 point 0 0 dollars
B
4 point 0 0 dollars
C
18 point 0 0 dollars
D
3 point 0 0 dollars
6

The amount of a radioactive substance remaining after t years is given by the function f of t is equal to m times 0 point 5 raised to the t over h power , where m is the initial mass and h is the half-life in years. Cobalt- 60 has a half-life of about 5 point 3 years. Which equation gives the mass of a 50 milligrams Cobalt- 60 sample remaining after 10 years, and approximately how many milligrams remain?

A
f of 10 is equal to 5 point 3 times 0 point 5 to the 5th power ; 0 point 2 milligrams
B
f of 10 is equal to 5 point 3 times 0 point 5 raised to the 0 point 2 power ; 4 point 6 milligrams
C
f of 10 is equal to 50 times 0 point 5 0 raised to the 0 point 5 3 power ; 34 point 6 milligrams
D
f of 10 is equal to 50 times 0 point 5 raised to the 10 over 5 point 3 power ; 13 point 5 milligrams
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 cap 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
Image with description A graph shows change in dimensions (units) labeled 0 to 10 on the horizontal axis and area (square units) labeled 0 to 50 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.
B
Image with description A graph shows change in dimensions (units) labeled 0 to 10 on the horizontal axis and area (square units) labeled 0 to 50 on the vertical axis. A curved line decreases from 0 to 9 units.
C
Image with description A graph shows change in dimensions (units) labeled 0 to 10 on the horizontal axis and area (square units) labeled 0 to 50 on the vertical axis. A straight line decreases from 0 to 9 units.
D
Image with description A graph shows change in dimensions (units) labeled 0 to 10 on the horizontal axis and area (square units) labeled 0 to 50 on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
8

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
Image with description A graph shows dropping time (seconds) labeled 0 to 10 on the horizontal axis and object speed (meters per second) labeled 0 to 100 on the vertical axis. A line increases from 0 to 4.5 seconds.
B
Image with description A graph shows dropping time (seconds) labeled 0 to 10 on the horizontal axis and object speed (meters per second) labeled 0 to 100 on the vertical axis. A line decreases from 0 to 4 seconds.
C
Image with description A graph shows dropping time (seconds) labeled 0 to 10 on the horizontal axis and object speed (meters per second) labeled 0 to 100 on the vertical axis. A line increases from 0 to 10 seconds.
D
Image with description A graph shows dropping time (seconds) labeled 0 to 10 on the horizontal axis and object speed (meters per second) labeled 0 to 100 on the vertical axis. A line decreases from 1 to 9 seconds.
9

The amount of a radioactive substance remaining after t years is given by the function f of t is equal to m times 0 point 5 raised to the t over h power , where m is the initial mass and h is the half-life in years. Iron has a half-life of 2 point 7 years. Which equation gives the mass of a 200 mathrm mg iron sample remaining after t years, and approximately how many milligrams remain after 12 years?

A
f of t is equal to 2 point 7 times 0 point 5 to the t th power ; 0 point 0 0 0 7 mathrm mg
B
f of t is equal to 2 point 7 times 0 point 5 raised to the t over 200 power ; 2 point 6 mathrm mg
C
f of t is equal to 200 times 0 point 5 to the t th power ; 0 point 0 5 mathrm mg
D
f of t is equal to 200 times 0 point 5 raised to the t over 2 point 7 power ; 9 point 2 mathrm mg
10

Which type of function should Sophia use to model the shape of the lens?

A
quadratic
B
square root
C
exponential
D
linear
11

Which type of function should Sophia use to model the shape of the lens?

A
quadratic
B
linear
C
exponential
D
square root
12

Which situation could be represented on the graph?

A
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.
B
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.
C
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.
D
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.
13

The amount of a radioactive substance remaining after t years is given by the function f of t is equal to m times 0 point 5 raised to the t over h power , where m is the initial mass and h is the half-life in years. Iron has a half-life of 2 point 7 years. Which equation gives the mass of a 200 mathrm mg iron sample remaining after t years, and approximately how many milligrams remain after 12 years?

A
f of t is equal to 2 point 7 times 0 point 5 raised to the t over 200 power ; 2 point 6 mathrm mg
B
f of t is equal to 2 point 7 times 0 point 5 to the t th power ; 0 point 0 0 0 7 mathrm mg
C
f of t is equal to 200 times 0 point 5 to the t th power ; 0 point 0 5 mathrm mg
D
f of t is equal to 200 times 0 point 5 raised to the t over 2 point 7 power ; 9 point 2 mathrm mg
14

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? Choose two correct answers.

A
The function relating snow depth to water depth is quadratic.
B
The data can be represented by f of x is equal to 0 point 2 to the x th power .
C
A line through the points will pass through 0 comma 0 .
D
The points on a graph representing the relationship lie on a line.
E
There is 0 point 4 inch of water to every 1 inch of snow.
15

What is the hourly revenue if there is no decrease in price?

A
200 dollars
B
225 dollars
C
150 dollars
D
100 dollars
16

Which type of function should Sophia use to model the shape of the lens?

A
square root
B
linear
C
quadratic
D
exponential
17

Which type of function should Sophia use to model the shape of the lens?

A
square root
B
quadratic
C
linear
D
exponential
18

What is the amount spent on each visit to the smoothie shop?

A
3 point 0 0 dollars
B
4 point 0 0 dollars
C
18 point 0 0 dollars
D
6 point 0 0 dollars
19

How many points will Brandon earn on day 8 if he works out each of the previous 7 days?

A
32
B
64
C
128
D
8
20

What is the hourly revenue if there is no decrease in price?

A
100 dollars
B
150 dollars
C
200 dollars
D
225 dollars

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