The variable interest rate on a student loan changes each July 1 based on the bank prime loan rate. For the years 1992-2007, this rate can be approximated by the model r(x) = -0.115x² + 1.183x + 5.623, where x is the number of years since 1992 and r is the interest rate as a percent.

(a) Use a graphing utility to estimate the highest rate during this time period. During which year was the interest rate the highest?

(b) Use the model to estimate the rate in 2010. Does this value seem reasonable?