Section 3.3 Slope of a Line and Rate of Change 247 Concept 4: Applications of Slope: Rate of Change 73. For a recent year, the average earnings for male workers between the ages of 25 and 34 with a high school diploma was $32,000. Comparing this value in constant dollars to the average earnings 15 yr later showed that the average earnings have decreased to $29,600. Find the average rate of change in dollars per year. Hint: Use the ordered pairs (0, 32000) and (15, 29600). The average rate of change is $160 per year. 74. In 1985, the U.S. Postal Service charged $0.22 for first class letters and cards up to 1 oz. By 2013, the price had increased to $0.46. Let x represent the year, and y represent the cost for 1 oz of first class postage. Find the average rate of change of the cost per year. Round to three decimal places. 75. In 1985, there were 539 thousand male inmates in federal and state prisons. By 2010, the number increased to 1714 thousand. Let x represent the year, and let y represent the number of prisoners (in thousands). (See Example 8.) a. Using the ordered pairs (1985, 539) and (2010, 1714), find the slope of the line. m 47 b. Interpret the slope in the context of this problem. The number of male prisoners increased at a rate of 47 thousand per year during this time period. 76. In the year 1985, there were 30 thousand female inmates in federal and state prisons. By 2010, the number increased to 120 thousand. Let x represent the year, and let y represent the number of prisoners (in thousands). a. Using the ordered pairs (1985, 30) and (2010, 120), find the slope of the line. m 3.6 b. Interpret the slope in the context of this problem. 1800 1600 1400 1200 1000 800 600 400 200 0 539 Number of Male State and Federal Prisoners (in thousands) 1985–2010 1985 1990 1995 2000 2005 2010 140 120 100 80 40 20 Number of Female State and Federal Prisoners (in thousands) 1985–2010 d 0.2t Distance Between Lightning Strike and an Observer d 0.2t d 2 mi 3 mi Writing Translating Expression Geometry Scientific Calculator Video 1714 x y Prisoners (in thousands) Year (Source: U.S. Bureau of Justice Statistics) (Source: U.S. Bureau of Justice Statistics) 0 1985 1990 1995 2000 2005 2010 60 30 120 x y Prisoners (in thousands) Year The number of female prisoners increased at a rate of 3.6 thousand per year during this time period. 77. The distance, d (in miles), between a lightning strike and an observer is given by the equation , where t is the time (in seconds) between seeing lightning and hearing thunder. 5 0 0 5 10 15 20 25 Distance (miles) Time (seconds) 4 3 2 1 t The cost increased at a rate of $0.009 per year. a. If an observer counts 5 sec between seeing lightning and hearing thunder, how far away was the lightning strike? 1 mi b. If an observer counts 10 sec between seeing lightning and hearing thunder, how far away was the lightning strike? c. If an observer counts 15 sec between seeing lightning and hearing thunder, how far away was the lightning strike? d. What is the slope of the line? Interpret the meaning of the slope in the context of this problem. The distance between a lightning strike and an observer increases by 0.2 mi for every additional second between seeing m 0.2; lightning and hearing thunder.
miller_introductory_algebra_3e_ch1_3
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