178 Chapter 2 Linear Equations in Two Variables and Functions Concept 2: Interpreting a Linear Model 11. Sound travels at approximately one-fifth of a mile per second.Therefore, the difference in time, x (in seconds), between seeing lightning and hearing thunder can be used to estimate the distance y (in miles) between a storm and an observer.The distance of the storm can be approximated by the equation y 0.2x, where x 0. (See Example 2.) a. Use the linear model to determine the distance between a storm and an observer for the following times between seeing lightning and hearing thunder: 4 sec, 12 sec, and 16 sec. b. If a storm is 4.2 mi away, how many seconds will pass between seeing lightning and hearing thunder? 12. The force y (in pounds) required to stretch a particular spring x in. beyond its rest (or “equilibrium”) position y 2.5x, 0 x 20. is given by the equation where a. Use the equation to determine the amount of force necessary to stretch the spring 6 in. from its rest position. How much force is necessary to stretch the spring twice as far? b. If 45 lb of force is exerted on the spring, how far will the spring be stretched? 13. The equation y 9.4x 35.7 represents the average amount y (in $) spent on video games per person in the United States where x is the number of years since 2006. a. Use the equation to approximate the average amount spent per person in the year 2010. b. Use the equation to approximate the average amount spent per person in the year 2008 and compare it with the actual amount spent of $55.80. Amount Spent on Video Games Per Person by Year 100 80 60 40 20 0 0 1 2 3 4 5 6 Amount Spent ($) Year (x 5 0 represents 2006) c. What is the slope of the line and what does it mean in the context of this problem? d. What is the y-intercept and what does it mean in the context of this problem? 14. Let y represent the average number of miles driven per year for passenger cars in the United States since 1980. Let x represent the year where corresponds to 1980, x 1 corresponds to 1981, and so on.The average yearly mileage for passenger cars can be approximated by the equation y 142x 9060, where x 0. x 0 a. Use the linear equation to approximate the average yearly mileage for passenger cars in the United States in the year 2005. 14,000 Average Yearly Mileage for Passenger Cars, United States, 1980–2010 y 142x 9060 b. Use the linear equation to approximate the average mileage for the year 1985, and compare it with the actual value of 9700 mi. c. What is the slope of the line and what does it mean in the context of this problem? d. What is the y-intercept and what does it mean in the context of this problem? y 5 9.4x 1 35.7 x y 12,000 10,000 8,000 6,000 4,000 2,000 0 0 5 10 15 20 25 30 Miles Driven Year (x 0 corresponds to 1980) x y
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