Science:Math Exam Resources/Courses/MATH101 C/April 2024/Question 15/Statement

Let $B(t)$ be the balance in a bank account that has been active for $t$ years. Due to a special promotional interest rate calculation, $B$ satisfies the differential equation $$\frac{\mathrm{d}B}{\mathrm{d}t}=(rt)B.$$

If $B(0)=\mathrm{\$}100$, find an explicit equation for $B(t),t\ge 0$. Your answer may only depend on $r$ and $t$.