When will the alligator population in the swamp reach four dozen?

[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.

Homework Statement

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?

Homework Equations

dP/dt=kP

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 :)

 

[Dick]

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