Chapter 1, Problem 1.30IP

Charge-Storage Device
A capacitor is a two-terminal device that can store electric charge. In a linear capacitor, the amount of charge stored is proportional to the voltage across the device. For a particular device the proportionality is $q\left(t\right)={10}^{-7}v\left(t\right).$  If $v\left(t\right)=0$ and $t<0$ and $v\left(t\right)=10\left(1-e^{-5000t}\right)$ for $t\ge 0,$ find the energy stored in the device at $t=100\text{μs}\text{.}$