The current $I$ in an electric circuit at time $t$ satisfies the differential equation \[4\frac{

Question

The current $I$ in an electric circuit at time $t$ satisfies the differential equation $$4\frac{\mathrm{d}I}{\mathrm{d}t}=2-3I.$$ Find $I$ in terms of $t$, given that $I=2$ when $t=0$. State what happens to the current in this circuit for large values of $t$.

Accepted Answer

(a) $I = \frac{2}{3} \left( 1 + 2e^{-\frac{3t}{4}} \right)$; (b) $I \rightarrow \frac{2}{3}$ as $t \rightarrow \infty$.

Differential Equations - Modelling involving Multiple Rates

Differential Equations - Modelling involving Multiple Rates