# Differential population decay

1. Apr 17, 2010

### synergix

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

The fish population in a lake is attacked by a disease at time t=0 with the result that the size P(t) of the population at time t:

dP/dt= -k*sqrt(P)

where k is a positive constant. If there were initially 90,000 fish in the lake and 40,000 were left after 6 weeks, when will the fish population be reduced to 10,000?

3. The attempt at a solution

integrate [(90,000->40,000) dP/sqrt(P)] = integrate [(0->t)-kdt]

then set t= 6 and solve for k

this was a question on a test I did not know how to do could you tell me if I am on the right track?

2. Apr 17, 2010

### pbandjay

I am uncertain that using limits of integration leads to the correct answer. You have this:

$$\displaystyle\int \frac{dP}{\sqrt{P}} = \displaystyle\int -k dt$$

where, after integrating, there will be two constants. Luckily there are two conditions.

Last edited: Apr 17, 2010