$2)(10$ pt$)$ Tuition at a major university rose from $\backslash (\backslash$$ $1,500/\backslash$mathrm$\{$yr$\}\backslash )$ in $1962$ to $\backslash (\backslash$$ $20,000/\backslash$mathrm$\{$yr$\}\backslash )$ in $1995.$

$($a$)(5$ pt$)$ What exponential rate of growth $($continuous compounding$)$ characterized that period? Assume the growth rate was constant during that period.

$($b$)(5$ pt $)$ If that growth rate were to continue for another $25$ years $($enough time for current students to have children in college!$),$ what would the tuition be$?$