Science:Math Exam Resources/Courses/MATH105/April 2011/Question 05 (b)/Statement

You open a savings account under the Escalator Plan with an initial deposit of $\$P$. The advantage of this plan is that the interest rate is not fixed, but grows proportionally with time as long as the account is alive. In other words, the money in the account collects interest at the annual rate of $rt$ at time $t,$ compounded continuously (here $r$ is a constant). You also keep adding money to the account in the form of a continuous deposit of $\$S(t)$ at time $t.$

Now suppose that $P=100$, $r=0.01$, and $S(t)=0.$ Under these assumptions, solve the initial value problem you wrote down in part (a).