An Australian24 study found that, if other factors are constant (education, experience

For Problems 14, find an equation for the line that passes through the given points.(0, 2) and (2, 3)

For Problems 14, find an equation for the line that passes through the given points.(0, 0) and (1, 1)

For Problems 14, find an equation for the line that passes through the given points.(2, 1) and (2, 3)

For Problems 14, find an equation for the line that passes through the given points.(4, 5) and (2,1)

For Problems 58, determine the slope and the y-intercept of the line whose equation is given.7y + 12x 2 = 0

For Problems 58, determine the slope and the y-intercept of the line whose equation is given.3x + 2y = 8

For Problems 58, determine the slope and the y-intercept of the line whose equation is given.12x = 6y + 4 s

For Problems 58, determine the slope and the y-intercept of the line whose equation is given.4y + 2x +8 = 0

Figure 1.21 shows four lines given by equation y = b + mx. Match the lines to the conditions on the parameters m and b. (a) m > 0, b > 0 (b) m < 0, b > 0 (c) m > 0, b < 0 (d) m < 0, b < 0 l1 l2 l l3 4 x y Figure 1.21 1

(a) Which two lines in Figure 1.22 have the same slope? Of these two lines, which has the larger y-intercept? (b) Which two lines have the same y-intercept? Of these two lines, which has the larger slope? l1 l2 l3 l4 l5 x y Figure 1.22 1

A citys population was 30,700 in the year 2010 and is growing by 850 people a year. (a) Give a formula for the citys population, P, as a function of the number of years, t, since 2010. (b) What is the population predicted to be in 2020? (c) When is the population expected to reach 45,000? 1

A company rents cars at $40 a day and 15 cents a mile. Its competitors cars are $50 a day and 10 cents a mile. (a) For each company, give a formula for the cost of renting a car for a day as a function of the distance traveled. (b) On the same axes, graph both functions. (c) How should you decide which company is cheaper? 1

Figure 1.23 shows the distance from home, in miles, of a person on a 5-hour trip. (a) Estimate the vertical intercept. Give units and interpret it in terms of distance from home. (b) Estimate the slope of this linear function. Give units, and interpret it in terms of distance from home. (c) Give a formula for distance,D, fromhome as a function of time, t in hours. 1 2 3 4 5 200 400 600 t (hours) D (miles) Figure 1.23 1

Which of the following tables could represent linear functions? (a) x 0 1 2 3 y 27 25 23 21 (b) t 15 20 25 30 s 62 72 82 92 (c) u 1 2 3 4 w 5 10 18 28 1

For each table in Problem 14 that could represent a linear function, find a formula for that function. Reference:

A cell phone company charges amonthly fee of $25 plus $0.05 per minute. Find a formula for the monthly charge, C, in dollars, as a function of the number ofminutes, m, the phone is used during the month. 1

Annual revenue R from McDonalds restaurants worldwide can be estimated by R = 19.1+1.8t, where R is in billion dollars and t is in years since January 1, 2005.13 (a) What is the slope of this function? Include units. Interpret the slope in terms of McDonalds revenue. (b) What is the vertical intercept of this function? Include units. Interpret the vertical intercept in terms of McDonalds revenue. (c) What annual revenue does the function predict for 2015? (d) When is annual revenue predicted to hit 35 billion dollars? 1

A companys pricing schedule in Table 1.5 is designed to encourage large orders. (A gross is 12 dozen.) Find a formula for: (a) q as a linear function of p. (b) p as a linear function of q. Table 1.5 q (order size, gross) 3 4 5 6 p (price/dozen) 15 12 9 6 1

World milk production rose at an approximately constant rate between 2000 and 2012.14 See Figure 1.24. (a) Estimate the vertical intercept and interpret it in terms of milk production. (b) Estimate the slope and interpret it in terms of milk production. (c) Give an approximate formula for milk production, M, as a function of t. 2 4 6 8 10 12 350 600 t (years since 2000) M (million tons) Figure 1.24 2

The percentage of people, P, below the poverty level in the US15 is given in Table 1.6. (a) Find a formula for the percentage in poverty as a linear function of time in years since 2000. (b) Use the formula to predict the percentage in poverty in 2006. (c) What is the difference between the prediction and the actual percentage, 12.3%? Table 1.6 Year (since 2000) 0 1 2 3 P (percentage) 11.3 11.7 12.1 12.5 2

World grain production was 1241 million tons in 1975 and 2048 million tons in 2005, and has been increasing at an approximately constant rate.16 (a) Find a linear function for world grain production, P, in million tons, as a function of t, the number of years since 1975. (b) Using units, interpret the slope in terms of grain production. (c) Using units, interpret the vertical intercept in terms of grain production. (d) According to the linear model, what is the predicted world grain production in 2015? (e) According to the linear model, when is grain production predicted to reach 2500 million tons? 2

Annual sales of music compact discs (CDs) have declined since 2000. Sales were 942.5 million in 2000 and 384.7 million in 2008.17 (a) Find a formula for annual sales, S, inmillions ofmusic CDs, as a linear function of the number of years, t, since 2000. (b) Give units for and interpret the slope and the vertical intercept of this function. (c) Use the formula to predict music CD sales in 2012. 2

Search and rescue teams work to find lost hikers. Members of the search team separate and walk parallel to one another through the area to be searched. Table 1.7 shows the percent, P, of lost individuals found for various separation distances, d, of the searchers.18 Table 1.7 Separation distance d (ft) 20 40 60 80 100 Approximate percent found, P 90 80 70 60 50 (a) Explain how you know that the percent found, P, could be a linear function of separation distance, d. (b) Find P as a linear function of d. (c) What is the slope of the function? Give units and interpret the answer. (d) What are the vertical and horizontal intercepts of the function? Give units and interpret the answers. 2

In a California town, the monthly charge for waste collection is $8 for 32 gallons of waste and $12.32 for 68 gallons of waste. (a) Find a linear formula for the cost, C, ofwaste collection as a function of the number of gallons of waste, w. (b) What is the slope of the line found in part (a)? Give units and interpret your answer in terms of the cost of waste collection. (c) What is the vertical intercept of the line found in part (a)? Give units and interpret your answer in terms of the cost of waste collection. 2

The number of species of coastal dune plants in Australia decreases as the latitude, in S, increases. There are 34 species at 11S and 26 species at 44S.19 (a) Find a formula for the number, N, of species of coastal dune plants in Australia as a linear function of the latitude, l, in S. (b) Give units for and interpret the slope and the vertical intercept of this function. (c) Graph this function between l = 11S and l = 44S. (Australia lies entirely within these latitudes.) 2

Table 1.8 gives the average weight, w, in pounds, of American men in their sixties for height, h, in inches.20 (a) How do you know that the data in this table could represent a linear function? (b) Find weight, w, as a linear function of height, h. What is the slope of the line? What are the units for the slope? (c) Find height, h, as a linear function of weight, w. What is the slope of the line? What are the units for the slope? Table 1.8 h (inches) 68 69 70 71 72 73 74 75 w (pounds) 166 171 176 181 186 191 196 201 2

Which of the following is the correct statement? (a) As you age, your maximum heart rate decreases by one beat per year. (b) As you age, your maximum heart rate decreases by one beat per minute. (c) As you age, your maximum heart rate decreases by one beat per minute per year. 2

Which of the following is the correct statement for a male and female of the same age? (a) Their maximum heart rates are the same. (b) The males maximum heart rate exceeds the females. (c) The females maximum heart rate exceeds the males. 2

What can be said about the ages of a male and a female with the same maximum heart rate? 3

Recently21 it has been suggested that a more accurate predictor of MHR for both males and females is given by MHR = 208 0.7a. (a) At what age do the old and new formulas give the same MHR for females? For males? (b) Which of the following is true? (i) The new formula predicts a higher MHR for young people and a lower MHR for older people than the old formula. (ii) The new formula predicts a lower MHR for young people and a higher MHR for older people than the old formula. (c) When testing for heart disease, doctors ask patients to walk on a treadmill while the speed and incline are gradually increased until their heart rates reach 85 percent of the MHR. For a 65-year-old male, what is the difference in beats per minute between the heart rate reached if the old formula is used and the heart rate reached if the new formula is used? 3

Experiments22 suggest that the female MHR decreases by 12 beats per minute by age 21, and by 19 beats per minute by age 33. Is this consistent with MHR being approximately linear with age? 3

Experiments23 suggest that the male MHR decreases by 9 beats perminute by age 21, and by 26 beats per minute by age 33. Is this consistent with MHR being approximately linear with age? 3

Let y be the percent increase in annual US national production during a year when the unemployment rate changes by u percent. (For example, u = 2 if unemployment increases from 4% to 6%.) Okuns law states that y = 3.5 2u. (a) What is the meaning of the number 3.5 in Okuns law? (b) What is the effect on national production of a year when unemployment rises from 5% to 8%? (c) What change in the unemployment rate corresponds to a year when production is the same as the year before? (d) What is the meaning of the coefficient 2 in Okuns law? 3

An Australian24 study found that, if other factors are constant (education, experience, etc.), taller people receive higher wages for the same work. The study reported a height premium for men of 3% of the hourly wage for a 10 cm increase in height; for women the height premium reported was 2%. We assume that hourly wages are a linear function of height, with slope given by the height premium at the average hourly wage for that gender. (a) The average hourly wage25 for a 178 cm Australian man is AU$29.40. Express the average hourly wage of an Australian man as a function of his height, x cm. (b) The average hourly wage for a 164 cm Australian woman is AU$24.78. Express the average hourly wage of an Australian woman as a function of her height, y cm. (c) What is the difference in average hourly wages between men and women of height 178 cm? (d) Is there a height for which men and women are predicted to have the same wage? If so, what is it?