In a pristine lake with carrying capacity K and fishing allowed, the logistic differential equation for the population N(t) of fish at time t(in days) is dN/dt= rN(1-(N/K) - H.

Question

H= the fish harvested from the lake each day.

If H= 3/16rK find all of the equilibria for the differential equation.
*I got (1/4) and (3/4).

What will happen to the fish population after a long time if the current population equals half of the carrying capacity?
*Do I solve the differential here?

If the rate of fish harvested is increased from H=3/16 rK fish per day to a larger number, how will the curve that you drew be affected ?
*The graph(dN/dt vs N) I drew is an upside down parabola shape that goes through the x-axis at (1/4) and (3/4)

If H is large enough, then the fish populations is guaranteed to go extinct. Find the smallest value of H for which the fish population is guaranteed to go extinct.
*No idea how to do this question

Answer 1

yesh - why don't we get part B at this point. Solve the DE.
Also, you might google logistic growth to see how the other parameters are used.

Answer 2

ummm could you possibly walk me through on how i would solve the DE...?
Thank you for your response!