Chapter 12.2, Problem 40E

Earned run average A baseball pitcher’s earned run average (ERA) is A(e, i) = 9e/i, where e is the number of earned runs given up by the pitcher and i is the number of innings pitched. Good pitchers have low ERAs. Assume that e ≥ 0 and i > 0 are real numbers.

a.    The single-season major league record for the lowest ERA was set by Dutch Leonard of the Detroit Tigers in 1914. During that season, Dutch pitched a total of 224 innings and gave up just 24 earned runs. What was his ERA?

b.    Determine the ERA of a relief pitcher who gives up 4 earned runs in one-third of an inning.

c.    Graph the level curve A(e, i) = 3 and describe the relationship between e and i in this case.