AnswersAZ-Common Core Algebra II BLinear Growth vs. Exponential Growth

Linear Growth vs. Exponential Growth Answers

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1
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Mary creates a table of values for a function and plots the points. She finds that the difference in the y values is the same. What kind of function did she graph?

A
linear
B
quadratic
C
square root
D
exponential
2
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The graphs of y = 4x and y = 4x are shown below. In general, how does the growth of y = 4x compare to the growth of y = 4x?

Question illustration
A
The function y = 4x is growing slower than y = 4x.
B
The function y = 4x is growing faster than y = 4x.
C
The functions y = 4x and y = 4x are growing at the same rate.
D
The function y = 4x is growing faster than y = 4x.
3

Which graph represents a linear function?

A
mc002-1.jpg
Option A
B
mc002-2.jpg
Option B
C
mc002-3.jpg
Option C
D
mc002-4.jpg
Option D
4

The graph below shows two different deer populations over the same ten year period. Deer PopulationWhich of the following answers is the best description for the deer population with the greatest growth rate:

Question illustration
A
The blue line shows a deer population that grew with an exponential growth rate. In the first year the population increased by only one deer, but between years seven and eight the population grew by two deer, showing that the growth rate continuously doubles.
B
The blue line shows a deer population that grew with a linear growth rate, because the graph shows that the population increased by approximately one deer per year.
C
The red line shows a linear growth rate, because an approximate straight line estimates a growth rate of five deer per year.
D
The red line demonstrates an exponential growth rate, because the growth rate for the deer population is itself continuously increasing.
5

Chen is given the graph below.What type of graph is shown, and what is the growth factor?

Question illustration
A
linear function; growth factor of 2
B
linear function; growth factor of 4
C
exponential function; growth factor of 2
D
exponential function; growth factor of 4
6

The table below represents a function. x12345y612182430 Which statement would best describe the graph of the function?

A
The graph is a straight line that has a slope of 6.
B
The graph is a horizontal line at y = 6.
C
The graph starts flat but curves steeply upward.
D
The graph is a parabola that opens upward.
7

What kind of growth model (pattern) is shown in the table? xy152253125462553,125

A
square root
B
linear
C
exponential
D
quadratic
8

Which graph represents an exponential function?

A
mc001-1.jpg
Option A
B
mc001-2.jpg
Option B
C
mc001-3.jpg
Option C
D
mc001-4.jpg
Option D
9

Which table represents an exponential function?

A
mc019-1.jpg
Option A
B
mc019-2.jpg
Option B
C
mc019-3.jpg
Option C
D
mc019-4.jpg
Option D
10

Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans.Plan A: Raise the price by $0.05 each week until the price reaches $8.00.Plan B: Raise the price by 10 percent each week until the price reaches $8.00.Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00.Plan D: Raise the price by $0.25 each week until the price reaches $8.00.Which plan will result in the price of the bagels reaching $8.00 fastest?

A
plan A
B
plan B
C
plan C
D
plan D
11

What kind of growth model (pattern) is shown in the table? xy152253125462553,125

A
square root
B
linear
C
exponential
D
quadratic
12

Which of the following best describes how the y values are changing over each interval?xy1428312416520

A
They are increasing by 4 each time.
B
They are increasing by 6 each time.
C
They are being multiplied by 2 each time.
D
They are being multiplied by 4 each time.
13

The table below represents a function. x12345y612182430 Which statement would best describe the graph of the function?

A
The graph is a straight line that has a slope of 6.
B
The graph is a horizontal line at y = 6.
C
The graph starts flat but curves steeply upward.
D
The graph is a parabola that opens upward.
14

The graph below shows two different deer populations over the same ten year period. Deer PopulationWhich of the following answers is the best description for the deer population with the greatest growth rate:

Question illustration
A
The blue line shows a deer population that grew with an exponential growth rate. In the first year the population increased by only one deer, but between years seven and eight the population grew by two deer, showing that the growth rate continuously doubles.
B
The blue line shows a deer population that grew with a linear growth rate, because the graph shows that the population increased by approximately one deer per year.
C
The red line shows a linear growth rate, because an approximate straight line estimates a growth rate of five deer per year.
D
The red line demonstrates an exponential growth rate, because the growth rate for the deer population is itself continuously increasing.
15

Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans.Plan A: Raise the price by $0.05 each week until the price reaches $8.00.Plan B: Raise the price by 10 percent each week until the price reaches $8.00.Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00.Plan D: Raise the price by $0.25 each week until the price reaches $8.00.Which plan will result in the price of the bagels reaching $8.00 fastest?

A
plan A
B
plan B
C
plan C
D
plan D
16

The graphs of y = 4x and y = 4x are shown below. In general, how does the growth of y = 4x compare to the growth of y = 4x?

Question illustration
A
The function y = 4x is growing slower than y = 4x.
B
The function y = 4x is growing faster than y = 4x.
C
The functions y = 4x and y = 4x are growing at the same rate.
D
The function y = 4x is growing faster than y = 4x.
17

Which graph represents a linear function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
18

The table below represents a function. x12345y116642561,024 Which statement would best describe the graph of the function?

A
The graph is a straight line that has a slope of 8.
B
The graph is a horizontal line at y = 16.
C
The graph starts flat but curves steeply upward.
D
The graph is a parabola that opens upward.
19

Mary creates a table of values for a function and plots the points. She finds that the difference in the y values is the same. What kind of function did she graph?

A
linear
B
quadratic
C
square root
D
exponential
20

Margo is given the graph below.What type of graph is shown, and what is the growth factor?

Question illustration
A
linear function; growth factor of 2
B
linear function; growth factor of 4
C
exponential function; growth factor of 2
D
exponential function; growth factor of 4

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