Chapter 1 Homework

Math 96 – Applied Algebra 2 – BunnellSection 1.1

1) 1.1.1 The amount of electricity (measured in Kilowatt-hours, KWH) a home uses each month is affected by the temperature difference inside versus outside (measured in heating degree days, HDD). (if it is 60 degrees outside and you heat your house to 72 degrees for 5 days that is 12 x 5 = 60 HDD).

a) Which variable is most appropriate to pick as the dependent variable. Which variable should be the independent variable?

b) Create a scatterplot for the data and a separate sheet of graph paper. Be sure to label the axes, title the graph, and position the independent and dependent variables correctly.

c) Find the average rate of change between the data points with 133 and 561 degree days, accurate to 1 decimal places. Interpret the average rate of change in complete sentences.

d) Add a linear trend line to the graph.e) Choose two representative points from your trend line (not necessarily data points). Find the

slope of the trend line and explain the meaning of the slope in context.

Heating Degree

Days (HDD)

KWH Used

714 1799

469 1269

386 1160

266 860

133 804

62 696

7 677

5 666

87 736

354 1071

561 1602

968 2060

2) 1.1.3 A forester takes measurements in a grove of trees. Naturally older trees also have larger volumes.

a) Which variable should be the independent and dependent variables?

b) Create a scatterplot for the data on a separate sheet of graph paper. Be sure to label the axes, title the graph, and position the independent and dependent variables correctly.

c) Find the average rate of change between the youngest and oldest trees, accurate to 1 decimal places.

f) Add a linear trend line to the graph.

3) 1.1.10 Health costs are steadily rising in the United States.

a) Create a scatterplot. (include up to the year 2020)

b) Find the average rate of change between the data points at years 2000 and 2008.

c) Add a trend line to the graph.d) Choose two representative points from your trend line to find the

slope of the line. Explain the meaning of the slope in context.

e) Use your trend line to make a prediction for the health expenditure you might expect per person in 2020.

Section 1.2

4) 1.2.1 (Revisiting problem 1) The Kilowatt-hours (KWH) of electricity a home uses each month are dramatically affected by the temperature difference inside versus outside (measured in degree days).

a) Find the equation of the line passing through the lowest and highest degree day. Note: data is not in order. Round slope and y-intercept to 2 decimal places.

b) Does this seem to be a good model for the trend? (You can look back at your scatterplot in problem 1.) Do you think you can always get the best trend line by this method? Why or why not?

5) 1.2.3 (Revisiting problem 2) Consider the data set from problem 2, comparing a tree’s age to its volume.

a) Find the equation of the line through two representative points from the trend line.

b) Interpret the slope of your equation.

Heating Degree

Days (HDD)

KWH Used

714 1799

469 1269

386 1160

266 860

133 804

62 696

7 677

5 666

87 736

354 1071

561 1602

968 2060

6) 1.2.5 The winning Olympic discus throw is recorded through the 1900’s rounded to the nearest foot. Consider 1900 to be year 0 for your calculations.

a) Find the equation of the line through two representative points from the trend line. Round slopes and y-intercepts to 2 decimal places.

a) Interpret the meanings of the slope and y-ingercept of the line.

b) Which 2 years had the largest rate of change? Calculate and interpret this rate of change.

Section 1.3

7) 1.3.1 The flow rate in gallons per minute (GPM) is shown in the table as a function of the horizontal discharge distance (A) in inches for various pipe diameters. You only need to consider the 2” pipe.

Round slope and y-intercept to 3 decimal places.

a) Find the equation for the trend line using the regression feature of your graphing calculator.

b) Use your equation to predict the flow rate for a horizontal discharge of 24 inches, accurate to 1 decimal place. Does this seem reasonable?

c) Use your equation to predict the horizontal distance (A) for a flow rate of 120 GPM, accurate to 1 decimal place. Does this seem reasonable?

8) 1.3.5 (Revisiting problem 2) A tree’s age and volume are related linearly as shown in the graph below.

Flow Rate (GPM)

a) Find the equation for the trend line using the regression feature of your graphing calculator. Round slopes and y-intercepts to 3 decimal places.

a) Use your regression equation to predict the volume of a 15 year old tree, accurate to 1 decimal place.

b) Use your regression equation to predict the age of a tree with a 500 m3 volume, rounded to the nearest year. Comment on the reasonableness of this prediciton.

9) 1.3.7 (Revisiting problem 6) The winning Olympic discus throw is recorded through the 1900’s rounded to the nearest foot.

Round slopes and y-intercepts to 2 decimal places

a) Consider 1900 to be year 0 and find the equation for the trend line using the regression feature of your graphing calculator.

b) Use your regression equation to predict the winning throw at the 2020 Olympics, accurate to the tenth place. Comment on the reasonableness of this prediciton.

c) Use your regression equation to predict the year the winning throw will reach 280 feet, accurate to the nearest year. Comment on the reasonableness of this prediciton.

Extra Stuff

10)Graph each equation.a. y=2x−1

b. y=−13x+4

11)Find the equation of the line passing through (−1 ,−2) and (5,6).

12)As a nurse takes on more patients, the chance that his/her patients die increases. If the Patient-to-Nurse ratio is represented by x and the percent increase in patient mortality I represented by ythen,

y=6x−22

c. Use the equation to determine the percentage increase in patient mortality if the patient-to-nurse ratio is 6.

d. If a Hospital wants to ensure that it does not increase patient mortality by more than 7 percent, what should the patient-to-nurse ratio be?

13)Consider the equation,p=1.1d+8.81

e. Find p when d=4.

f. Find d when p=25.3.

g. Solve the equation for d .