The population P=P(t) at time t of a species follows dPdt=0.5P-450.

Question

The population $P=P(t)$ at time $t$ of a species follows $\dfrac{dP}{dt}=0.5P-450$. If $P(0)=850$, the time at which population becomes zero is:

Accepted Answer

$$\int_0^t\frac{dP}{P-900}=\int_0^t\frac{dt}{2} \implies \ln|P(t)-900|-\ln|{-50}| = \frac{t}{2}.$$

For $P(t)=0$: $\ln\dfrac{900}{50}=\dfrac{t}{2} \implies t=2\ln18$.

Solutions · 1