AnswersCR27 ALG 1-1200310-S2-Degele-VOL7006PIntroduction to Modeling with Functions

Introduction to Modeling with Functions Answers

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1
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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.
2
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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
3

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
4

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
5

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.
6

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
7

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
8

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
9

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
10

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

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