- #1

Lin Galido

If a constant number h of fish are harvested from a fishery per unit time, then a model for the population

P(t) of the fishery at time t is given by:

dP/dt = P(5-P) - h, P(0) = P0.

a. Solve for the IVP if h = 4.

b. Determine the value of P0 such that the fish population becomes extinct in finite time.

My solution so far:

dP/dt = 5p - p^2 -4

dp/(-p^2 +5p - 4) = dt

by integration: ln |p-4| /3 - ln |p-1|/3 = dt

ln |p-4| - ln |p-1| = 3 dt

ln |p-4| - ln |p-1| = 3t + C

At P(0) (when t =0)

ln |P0 -4| - ln |P0 -1| = 3(0) + C

C = ln |P0 -4| - ln |P0 -1|

t = (ln |P-4| - ln |P-1| - ln |P0 -4| - ln |P0 -1|) /3

I end here and I'm not really sure waht to do after.