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 $B(0)=\$100$, find an explicit equation for $B(t),\;\;t\geq 0$. Your answer may only depend on $r$ and $t$.