Let population p(t) satisfy dp(t)dt=12p(t)-200, p(0)=100.

Question

Let population $p(t)$ satisfy $\dfrac{dp(t)}{dt}=\dfrac12p(t)-200$, $p(0)=100$. Then $p(t)$ equals:

Accepted Answer

Separating and integrating: $\dfrac{p(t)}{2}-200 = ke^{t/2}$; using $p(0)=100$ gives $p(t)=400-300e^{t/2}$.

Solutions · 1