Modeling Population Growth: Solving for P(t) Using Integration

[gtfitzpatrick]

Homework Statement

a population P(t) is modeled by the equation dP/dt = 0.0004P(P-150), Find a formula which gives the population, P(t), at a general time t.

Homework Equations

The Attempt at a Solution

swapping over

dt=1/0.004P(P-150) dP
then i integrate both sides

dt becomes t+c but I'm i'm not sure how to integrate the the dP side, any pointers please?

 

[arildno]

Are you able to integrate $\int\frac{dx}{x}$?

 

[HallsofIvy]

First, 1/0.004= 250. You have
$$250\int\frac{dP}{P(P-250)}dP$$

Use "partial fractions". Write
$$\frac{1}{P(P-250)}= \frac{A}{P}+ \frac{B}{P- 250}$$
Find A and B and do it as two separate integrals.