# Science:Math Exam Resources/Courses/MATH105/April 2011/Question 05 (a)

MATH105 April 2011
Other MATH105 Exams

### Question 05 (a)

You open a savings account under the Escalator Plan with an initial deposit of ${\displaystyle \P}$. 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 ${\displaystyle rt}$ at time ${\displaystyle t,}$ compounded continuously (here ${\displaystyle r}$ is a constant). You also keep adding money to the account in the form of a continuous deposit of ${\displaystyle \S(t)}$ at time ${\displaystyle t.}$

Write down the initial value problem for the amount ${\displaystyle A(t)}$ in your account in time ${\displaystyle t.}$

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