Solved: Quarterback passer ratings One measurement of the

Chapter 12, Problem 72

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Quarterback passer ratings One measurement of the quality of a quarterback in the National Football League is known as the quarterback passer rating. The rating formula is R1c, t, i, y2 = 50 + 20c + 80t - 100i + 100y 24 , where c is the percentage of passes completed, t is the percentage of passes thrown for touchdowns, i is the percentage of intercepted passes, and y is the yards gained per attempted pass. a. In 2012, Green Bay quarterback Aaron Rodgers had the highest passer rating. He completed 67.21% of his passes, 7.07% of his passes were thrown for touchdowns, 1.45% of his passes were intercepted, and he gained an average of 7.78 yards per passing attempt. What was his passer rating in the 2012 season? b. If c, t, and y remained fixed, what happens to the quarterback passer rating as i increases? Explain your answer with and without mathematics. (Source: The College Mathematics Journal, 24, 5, Nov 1993)