An individual€™s income varies with his or her age. The following table shows the median income I of males of different age groups within the United States for 2006. For each age group, let the class midpoint represent the independent variable, x. For the class €œ65 years and older,€ we will assume that the class midpoint is 69.5.

(a) Use a graphing utility to draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables.

(b) Use a graphing utility to find the quadratic function of best fit that models the relation between age and median income.

(c) Use the function found in part (b) to determine the age at which an individual can expect to earn the most income.

(d) Use the function found in part (b) to predict the peak income earned.

(e) With a graphing utility, graph the quadratic function of best fit on the scatter diagram.

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Class Median Age Midpoint, x Income, / 15-24 years $10,964 19.5 25-34 years $32,131 29.5 35-44 years $42,637 39.5 45-54 years $45,693 49.5 55-64 years 59.5 $41,477 65 years and older $23,500 69.5