249 2.4 Linear Functions 71. (Modeling) Olympic Times for 5000-Meter Run The graph shows the winning times (in minutes) at the Olympic Games for the men’s 5000-meter run, together with a linear approximation of the data. Olympic Times for 5000-Meter Run (in minutes) 12.0 12.5 13.0 13.5 14.0 14.5 15.0 Data from The World Almanac and Book of Facts. 1920 1910 1930 1940 1950 1960 1970 1980 2000 2020 1990 2010 (a) An equation for a linear model, based on data from 1912–2016 (where x represents the year), is y = -0.01717x + 47.55. Determine the slope. (See Example 6.) What does the slope of this line represent? Why is the slope negative? (b) What reason might explain why there are no data points for the years 1916, 1940, and 1944? (c) The winning time for the 2000 Olympic Games was 13.59 min. What does the model predict? How far is the prediction from the actual value? 72. (Modeling) U.S. Radio Stations The graph shows the number of U.S. radio stations on the air, along with the graph of a linear function that models the data. Number of Stations U.S. Radio Stations 0 Data from Federal Communications Commission. 4000 2000 Year 6000 8000 10,000 12,000 14,000 16,000 1950 1960 1970 1980 1990 2000 2010 2020 (a) An equation for a linear model, based on data from 1950–2018 (where x = 0 represents 1950, x = 10 represents 1960, and so on) is y = 194.39x + 2871.7. Determine the slope. (See Example 6.) What does the slope of this line represent? Why is the slope positive? (b) Use the model in part (a) to predict the number of stations in 2022.
RkJQdWJsaXNoZXIy NjM5ODQ=