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+ 0.25t)
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(1-0.25t) + 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?