Chapter 6.3, Problem 73E

Investment A large corporation starts at time $t=0$ to invest part of its receipts at a rate of P dollars per year in a hind for future corporate expansion. The fund earns r percent interest per year compounded continuously. The rate of growth of the amount A in the fund is given by

$\frac{dA}{dt}=rA+P$

where $A=0$ when $t=0$. Solve this differential equation for

4 as a function of t