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Section5.2Homework.pdf

1.

Student: Kiare Mays Date: 06/15/20

Instructor: Valery Shemetov Course: MTH154 – Quantitative Reasoning (with MCR4)

Assignment: Section 5.2 Homework

(1) number of years number of gallons

Per Capita Beer Consumption

(2)

(3) years gallons

Per Capita Beer Consumption

(4) gallons. year. five years.

The decline in per capita beer consumption is shown in the scatter plot. (a) What is the slope of the linear trendline? (b) Interpret the slope in real world terms by filling in the blanks.

1975 1980 1985 1990 1995 2000 2005 2010 20.5

21 21.5

22 22.5

23 23.5

24 24.5

25

ga llo

ns

(a) The slope of the linear trendline is . (Type an integer or a decimal.)

(b) The (1) is changing by (2) (3) per (4)

years 281.75 − 0.13

Per Capita Beer Consumption

y = − 0.13x + 281.75

2.

3.

(1) Per Capita Entitlement Spending number of 2011$ number of years

(2)

(3) years 2011$

Per Capita Entitlement Spending

(4) year. decade. 2011$.

The amount the government spends per person on social programs (entitlement spending) has been steadily increasing in a certain country (all values 2011$): (a) What is the slope of the linear trendline? (b) Interpret the slope in real world terms by filling in the blanks.

1950 1960 1970 1980 1990 2000 2010 2020 $0.00

$1,000.00

$2,000.00

$3,000.00

$4,000.00

$5,000.00

$6,000.00

$7,000.00

$8,000.00

20 11

$

(a) The slope of the linear trendline is . (Type an integer or a decimal.)

(b) The (1) is changing by (2) (3) per (4)

− 210,276 107.6

(1) Average Strikeouts Per Team Per Game number of strikeouts

number of years

(2)

(3) Average Strikeouts Per Team Per Game years

strikeouts

(4) year. decade. strikeout.

The number of strikeouts in a baseball league has been on the rise since 1980. (a) What is the slope of the linear trendline? (b) Interpret the slope in real world terms by filling in the blanks.

1975 1980 1985 1990 1995 2000 2005 2010 2015 4

4.5

5

5.5

6

6.5

7

7.5

8

# st

rik eo

ut s

(a) The slope of the linear trendline is . (Type an integer or a decimal.)

(b) The (1) is changing by (2) (3) per (4)

0.0672 − 128.19

Government Entitlement Spending

y = 107.6x − 210,276

Average Strikeouts per Team per Game

y = 0.0672x − 128.19

4.

5.

(1)

Consider the graph to the right. a. In words, describe the function shown on the graph. b.Find the slope of the graph and express it as a rate of change. c. Briefly discuss the conditions under which a linear function is a realistic model for the given situation.

0 1 2 3 4 5 0

1

2

3

4

5

Time (hours)

R ai

n D

ep th

(i nc

he s)

a. Select the correct answer below.

A. According to the function, the rain depth increases by every .4 inches 1 hour B. According to the function, the rain depth decreases by every .4 inches 1 hour C. According to the function, the rain depth increases by every .1 inch 4 hours D. According to the function, the rain depth decreases by every .1 inch 4 hours

b. Calculate the slope and represent it as a rate of change.

rate of change (1) = (Type an integer or a fraction.)

c. Select the correct answer below.

A. It is a good model if the rate of the rainfall decreases over time.

B. It is a good model if the rate of the rainfall does not remain constant over time.

C. It is a good model if the rate of the rainfall remains constant over time.

D. It is a good model if the rate of the rainfall increases over time.

inch(es) per hour hour(s) per inch

Plot the two given points and then sketch the line that contains the points. Find the run and rise in going from the first point listed to the second point listed. Find the slope of the line.

( , ) and ( , ) − 8 − 3 − 3 − 23

Choose the correct graph below.

A.

-12 12

-36

36

x

y

B.

-12 12

-36

36

x

y

C.

-12 12

-36

36

x

y

D.

-12 12

-36

36

x

y

The run of the line is . (Type an integer or a simplified fraction.)

The rise of the line is . (Type an integer or a simplified fraction.)

The slope of the line is . (Type an integer or a simplified fraction.)

6.

7.

A person's annual salary increases by $ over -year period. Find the average rate of change of the salary per year.

11,000 an 11

The average rate of change is $ per year.

In response to rising concerns about identity theft, the number of models of paper shredders a company manufactures increased approximately steadily from models in to models in . Find the average rate of change of the number of shredder models manufactured per year between and .

4 1996 38 2006 1996 2006

The average rate of change of the number of paper shredders manufactured per year between and was .

1996 2006

(Type an integer or decimal rounded to two decimal places as needed.)

8. The number of country households that paid bills online was million in 2006 and has increased by about million per year. Let n be the number of households (in millions) that paid bills online at t years since 2006. Complete parts a. and b.

16 4

a. Is there a linear relationship between t and n? Explain. If the relationship is linear, find the slope and describe what it means in this situation.

Choose the correct answer below, and if necessary, fill in the answer box.

A. Yes. Since the rate of change of the number of country households that paid bills online per year is a constant million per year, the variables t and n are linearly related. The slope is

. The number of households that pay bills online has decreased by million per year.

4

B. Yes. Since the rate of change of the number of country households that paid bills online per year is a constant million per year, the variables t and n are linearly related. The slope is

. The number of households that pay bills online has increased by million per year.

4

C. No. Since the rate of change of the number of country households that paid bills online per year varries per year, the variables t and n are not linearly related.

b. Describe the Rule of Four as it applies to this situation.

i. Use an equation to describe the number of households (in millions) that paid bills online t years since 2006.

n (Type an expression using t as the variable.)=

ii. Use a table of values of t and n to describe the situation.

Years since 2006

t

Number of households (millions)

n 0 1 2 3 4

(Type integers or decimals.)

iii. Use a graph to describe the situation. Choose the correct graph below.

A.

0 5 0

100

t

n

B.

0 5 0

100

t

n

C.

0 5 0

100

t

n

D.

0 5 0

100

t

n

9.

10.

Let n be the number of oil refineries at t years since . A reasonable model of the number of oil refineries is n t .

2001 = − 3.42 + 135.55

a. What is the slope? What does it mean in this situation? b. What is the n-intercept? What does it mean in this situation? c. Predict the number of refineries in .2013

a. What is the slope?

m =

What does the slope mean in this situation?

A. It means the number of refineries in was about .2001 135.55 B. It means that the number of refineries are decreasing by about per year.135.55 C. It means the number of refineries in was about .2001 3.42 D. It means that the number of refineries are decreasing by about per year.3.42

b. What is the n-intercept?

(Type an ordered pair.)

What does the n-intercept mean in this situation?

A. It means that the number of refineries are decreasing by about per year.3.42 B. It means the number of refineries in was about .2001 3.42 C. It means that the number of refineries are decreasing by about per year.135.55 D. It means the number of refineries in was about .2001 135.55

c. Predict the number of refineries in .2013

The number of refineries will be about . (Round to the nearest whole number as needed.)

Let F be the temperature (in degrees Fahrenheit) at t hours after noon. The line in the figure shown below describes the relationship between t and F.

0 1 2 3 4 5 6 0

10

20

30

40

50

60

Hours

D eg

re es

F ah

re nh

ei t

t

F

Complete parts a. and b.

a. Is the rate of change of temperature per hour constant? Explain.

A. Yes because there is a linear relationship between t and F.

B. No because there is no linear relationship between t and F.

b. What is the rate of change of temperature per hour?

F° (Type an integer or decimal rounded to two decimal places as needed.)

11.

12.

The number of strikeouts in a baseball league has been on the rise since 1980. (a) What is the y-intercept of the linear trendline? (b) Interpret the y-intercept in real world terms.

1975 1980 1985 1990 1995 2000 2005 2010 2015 4

4.5

5

5.5

6

6.5

7

7.5

8

# st

rik eo

ut s

(a) The y-intercept of the linear trendline is . (Type an integer or a decimal.)

(b) Choose the correct answer below.

A. The Average Strikeouts Per Team Per Game in 0 CE was about , which makes no sense in real world terms.

4.5

B. The Average Strikeouts Per Team Per Game in 0 CE was , which makes no sense in real world terms.

− 141.87

C. The Average Strikeouts Per Team Per Game in 1975 was about .4.5 D. The Average Strikeouts Per Team Per Game in 1975 was , which makes no sense in

real world terms. − 141.87

The amount the government spends per person on social programs (entitlement spending) has been steadily increasing in a certain country (all values 2011$): (a) What is the y-intercept of the linear trendline? (b) Interpret the y-intercept in real world terms.

1950 1960 1970 1980 1990 2000 2010 2020 $0.00

$1,000.00

$2,000.00

$3,000.00

$4,000.00

$5,000.00

$6,000.00

$7,000.00

$8,000.00

20 11

$

(a) The y-intercept of the linear trendline is . (Type an integer or a decimal.)

(b) Choose the correct answer below.

A. The Per Capita Entitlement Spending was $1,000 (2011$) in 1950, which makes no sense in real world terms.

B. The Per Capita Entitlement Spending was (2011$) in 1950, which makes no sense in real world terms.

− $208,025

C. The Per Capita Entitlement Spending was (2011$) in 0 CE, which makes no sense in real world terms.

$208,025

D. The Per Capita Entitlement Spending was (2011$) in 0 CE, which makes no sense in real world terms.

− $208,025

Average Strikeouts per Team per Game

y = 0.0741x − 141.87

Government Entitlement Spending

y = 106.48x − 208,025

13. Water is steadily pumped out of a flooded basement. Let v be the volume of water (in thousands of gallons) that remains in the basement t hours after the water began to be pumped. A linear model is shown below.

-1 1 2 3 4 5 6 7 8 9 -4

4

8

12

16

20

24

28

32

Hours

Th ou

sa nd

s of

g al

lo ns

t

Complete parts a) through d).

a) How much water is in the basement after hours of pumping?

3

thousand gallons

b) After how many hours of pumping will thousand gallons remain in the basement?

6

hours

c) How much water was in the basement before any water was pumped out?

thousand gallons

d) After how many hours of pumping will all the water be pumped out of the basement?

hours

14. Let g be the number of gallons of gasoline that remain in a car's gasoline tank after the car has been driven d miles since the tank was filled. Some pairs of values of d and g are shown in the following table.

d (miles)

g (gallons)

20 12 40 10 60 8 80 6

100 4 120 2

Complete parts a. to e.

a. Create a scattergram of the data. Then draw a linear model.

Choose the correct scattergram below.

A.

0 160 0

16

d

g

B.

0 160 0

16

d

g

C.

0 160 0

16

d

g

D.

0 160 0

16

d

g

b. Estimate how much gasoline is in the tank after the driver has gone miles since last filling up.70

After the driver has gone miles since last filling up, there will be gallons of gasoline in the tank.

70

c. Estimate the number of miles driven since the tank was last filled if of gasoline in the tank.1 gallon remains

The driver drove miles since the tank was last filled if of gasoline in the tank.1 gallon is

d. Find the d-intercept of the model. What does it mean in this situation?

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

(Type an ordered pair.)

A. The d-intercept of the model is . The d-intercept

estimates the number miles after which the gasoline tank will be empty.

B. The d-intercept of the model is . The d-intercept

estimates the number of gallons of gasoline in the tank at the start of the trip.

e. Find the g-intercept of the model. What does it mean in this situation?

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

(Type an ordered pair.)

A. The g-intercept of the model is

g p . The g-intercept

estimates the number of gallons of gasoline in the tank at the start of the trip.

B. The g-intercept of the model is . The g-intercept

estimates the number miles after which the gasoline tank will be empty.

15.

16.

17.

A person earns a starting salary of $ thousand at a company. Each year, he receives a $ thousand raise. Let s be the salary (in thousands of dollars) after he has worked at the company for t years. Complete parts (a) through (e).

8 2

a. Complete the table to help find an equation for t and s. Show the arithmetic that helps to identify the pattern. (Do not include the $ symbol in your answers.)

Time at Company (years)

t

Salary (thousands of dollars)

s 0 +2 • 1 +2 • 2 +2 • 3 +2 • 4 +2 •

s   (Type an expression using t as the variable.)=

b. Perform a unit analysis of the equation found in part (a). Choose the correct answer below.

A. In the equation, the units on both sides are thousands of dollars, so the equation is correct. B. In the equation, the units on both sides are years, so the equation is correct. C. In the equation, the units on one side are thousands of dollars and the units on the other side

are years, so the equation is correct.

c. Graph the equation by hand.

Choose the correct graph below.

A.

0 8 0

24

t

s

B.

0 8 0

24

t

s

C.

0 8 0

24

t

s

D.

0 8 0

24

t

s

d. What is the s-intercept? What does it mean in this situation?

Select the correct choice below and fill in the answer box to complete your choice.

(Type an ordered pair.)

A. The s-intercept of the model is , and it represents the person's salary when he quits the job.

B. The s-intercept of the model is , and it represents the person's salary when he joined the company.

e. When will the person's salary be $ thousand?18

The person's salary will be $ thousand after years.18 (Type an integer or a decimal.)

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