CPM Homework Help : CALC Problem 11-114

The population P of mountain lions grow at a rate of $\frac { d P } { d t } = \frac { 1 } { 160 } P ( 40 - P )$ lions per year. At time $t = 0$ , there were $12$ lions. What is the population after three years?

Hint:

Partial fraction decomposition needs to be used.
$160\int\Big(\frac{A}{P}+\frac{B}{40-P}\Big)dP=\int dt$
Solve for $C$ when $t = 0$ and $P = 12$ .
Substitute your value for $C$ into the equation from Step 4 along with $t = 3$ . Then solve for $P$ .