Cost of Owning a Car Problem: Suppose you have fixed costs (car payments, insurance, and

Chapter 1, Problem 23

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Cost of Owning a Car Problem: Suppose you have fixed costs (car payments, insurance, and so on) of $300 per month and operating costs of $0.25 per mile you drive. The monthly cost of owning the car is given by the linear function c(x) = 0.25x + 300 where x is the number of miles you drive the car in a given month and c(x) is the number of dollars per month you spend. a. Find c(1000). Explain the real-world meaning of the answer. b. Find an equation for c1(x), where x now stands for the number of dollars you spend instead of the number of miles you drive. Explain why you can use the symbol c1 for the inverse relation. Use the equation of c1(x) to find c1(437) and explain its real-world meaning. c. Plot y1 = c(x) and y2 = c1(x) on the same screen, using function mode. Use a window of 0 x 1000 and use equal scales on the two axes. Sketch the two graphs, showing how they are related to the line y = x. 2