Integrals and initial-value problems?

I thought I understood this problem, until I solved it and got an answer of -4000 bacteria. Here is the problem:

A population of bacteria is changing at a rate of

*dP*/*dt* = 3000 / ( 1+ 0.25*t*)

where *t* is the time in days. The initial population is 1000. Write an equation that gives te population at any time *t*, and find the population when *t* = 3 days.

From this information I know that *P*(0) = 1000 and I went to integrate the function.

The equation I got was *P* = 3000 ln(1-0.25*t*) + k

But I don't think this is right because, well, -4158.5 just doesn't seem like a plausable answer to me. What should I have done differently?