# Homework Help: Practical integration

1. Feb 8, 2008

### gtfitzpatrick

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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?

2. Feb 8, 2008

### arildno

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

3. Feb 8, 2008

### 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.