Chapter 6.1, Problem 80E

Future Value In Exercises 79 and 80, find the future value of the income (in dollars) given by f(t) over $t_1$

years at annual interest rate r. If the function f represents a continuous investment over a period of t, years at an annual interest rate r (in decimal form) compounded continuously, then the future value of the investment is given by

Future value $=e^n,{\displaystyle {\int }_0^{t}f(t)e^{-rt}dt.}$.

$f(t)=3000e^{0.05t},r=10\%t_1=5\text{ years}$