Education and income: According to the U.S. Census Bureau, in 2004 the median (middle of the range) annual income of a high school graduate with no further education was about $37,000 per year. If we assume that it takes 4 years to earn a bachelor’s degree and 2 additional years to earn a master’s degree, the median annual income increases by 14% for each year spent toward successful completion of a degree. This describes a function I = I (y), where I is the median income in 2004 for a person with y years of college education.
a. Express in functional notation the median income in 2004 of an individual with an associate degree, which requires 2 years of college. Calculate the value.
b. Make a table of values that shows the median income in 2004 for individuals completing 0 through 4 years of college.
c. Make a graph of median income versus years of college completed. Be sure to provide appropriate labels.
d. Verify that the formula I = 37 × 1.14y thousand dollars, where y is the number of years of college completed, gives the same values as those you found in the table you made.
e. Using the formula given in part d, find the median income in 2004 of an individual who has a master’s degree.
f. Assuming it takes 3 years beyond the master’s degree to complete a Ph.D., and assuming the formula in part d applies, what was the median income of a Ph.D. in 2004?
g. In fact, the same rate of increase does not apply for the years spent on a Ph.D. The actual median income for a Ph.D. in 2004 was $100,000. Does that mean that the increase in median income for years spent earning a Ph.D. is higher or lower than 14% per year?