DE Population Models Question

1. Feb 8, 2010

forest125

Working on some DE homework and need a tad bit of guidance. I got fairly far, I'm just wondering what the next step is.

1. The problem statement, all variables and given/known data
The rate of change of an alligator population P is proportional to the square of P. The swamp contained a dozen alligators in 1988, two dozen in 1998. When will there be four dozen alligators in the swamp? What happens thereafter?

2. Relevant equations
dP/dt=kP

3. The attempt at a solution

Let P=the number of alligators in dozens
Let t=time in years, where 1988=0

dP/dt=kP^2

∫dP/P^2=∫kdt

-1/P=kt+C

P=-1/(kt+C)

Given that P(0)=1, C=-1

For P(10)=2, k=1/20 (2=-1/(10k-1))

So now could I say that P(t)=-1/((t/20)-1), let P(t)=4 and solve for t?

My concern isn't really to get the answer but that I am not understanding the procedure for this. I feel like I'm just stumbling through.

Any help is really appreciated greatly. Thanks :)

2. Feb 8, 2010

Dick

I think you are doing just fine. Yes, set P(t)=4 and solve for t.