AnswersAlgebraic ReasoningIntroduction to Modeling with Functions

Introduction to Modeling with Functions — Quiz Answers

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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

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