General: College Tuition The following graph shows the average annual college tuitio...

General: College Tuition The following graph shows the average annual college tuition costs (tuition and fees) for a year at a private nonprofit or public four-year college. The data are given for five-year intervals.

The tuition for a private college is approximated by the function f(x) = 650x²+3000x+12,000, where x is the number of five-year intervals since the academic year 1995–96 (so the years in the graph are numbered x = 0 through x = 3).

a. Use this function to predict tuition in the academic year 2020–21. [Hint: What x-value corresponds to that year?]

b. Find the derivative of this function for the x-value that you used in part (a) and interpret it as a rate of change in the proper units.

c. From your answer to part (b), estimate how rapidly tuition will be increasing per year in 2020–21.