The function f(x) = 2.91x + 20.1 models the median height, f(x), in inches, of boys who

Chapter 7, Problem 101

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The function f(x) = 2.91x + 20.1 models the median height, f(x), in inches, of boys who are x months of age. The graph of f is shown. 0 10 20 Age (months) 30 40 50 60 10 30 40 50 Median Height (inches) f(x) = 2.9x + 20.1 y x 20 Boys Heights Source: Laura Walter Nathanson, The Portable Pediatrician for Parents, 1994 Harper Perennial a. According to the model, what is the median height of boys who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for boys at 48 months is 40.8 inches. Does the model overestimate or underestimate the actual height? By how much? b. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth. c. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (b)? How is this difference shown by the graph?