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## Homework Statement

Sorry about the title; I accidentally hit enter instead of 'Shift'. It should read Logistic Modeling -- help integrating/solving for P

If P(0)=2, find P(90).

## Homework Equations

dP/dt=1/900P(9-P)

## The Attempt at a Solution

my solution looks like:

dP/(P(9-P))=1/900dt (seperable diff eq.)

1/9(ln(P)(9-P))=1/900 t+C (partial fractions and property ln M + ln N = ln MN)

lnP(9-P) = 1/100t+9C

P(9-P)= Ce^(1/100t) (exponentiated; 9C=C)

kinda stuck here (and I don't see how P ever stops growing.)

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