Baseball: earned-run average. A pitchers earned-run average (the average number of runs

Chapter 2, Problem 69

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Baseball: earned-run average. A pitchers earned-run average (the average number of runs given up every 9 innings, or 1 game) is given by where r is the number of earned runs allowed in n innings. Suppose that we fix the number of earned runs allowed at 4 and let n vary. We get a function given by a) Complete the following table, rounding to two decimal places: b) The number of innings pitched n is equivalent to the number of outs that a pitcher is able to get while pitching, divided by 3. For example, if the pitcher gets just 1 out, he is credited with pitching of an inning. Find Under what circumstances might this limit be plausible? c) Suppose a pitcher gives up 4 earned runs over two complete games, or 18 innings. Calculate the pitchers earned-run average, and interpret this result. While pitching for the St. Louis Cardinals in 1968, Bob Gibson had an earned-run average of 1.12, a record low.