Question:
The population $P=P(t)$ at time ' $t^{\prime}$ of a certain species follows the differential equation $\frac{d P}{d t}=0.5 \mathrm{P}-450$. If $\mathrm{P}(0)=850$, then the time at which population becomes zero is :
Correct Option: , 2
Solution:
$\frac{d p}{d t}=\frac{p-900}{2}$
$\int_{850}^{0} \frac{d p}{p-900}=\int_{0}^{t} \frac{d t}{2}$
$\ell n \mid P-900 \|_{850}^{0}=\frac{t}{2}$
$\ell n|900|-\ell n|50|=\frac{t}{2}$
$\frac{t}{2}=\ln |18|$
$\Rightarrow t=2 \ln 18$