Home > CALC > Chapter 11 > Lesson 11.3.2 > Problem11-114

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?

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 $P$.