Chapter 6, Problem 47RE

Continuous income stream. The rate of flow (in dollars per year) of a continuous income stream for a 5-year period is given by

$\begin{array}{cc}f\left(t\right)=2,500e^{0.05t}& 0\le \end{array}t\le 5$

(A) Graph y = f(t) over [0, 5] and shade the area that represents the total income received from the end of the first year to the end of the fourth year.

(B) Find the total income received, to the nearest dollar, from the end of the first year to the end of the fourth year.