Assignment:
Let P (t) represent a population of farm-raised catfish in a small lake at any time t in days.
(a) If the population grows according to the Malthusian model, and the time for the catfish population to triple if it grows by 10% in 45 days. Show all of you work. Your answer should be exact (it will contain logarithms)
(b) Suppose instead that the population grows logistically with r = 0:1 and a carrying capacity of 1500 catfish. Write the deferential equation modeling the change in the catfish population with respect to time.
(c) Edit your model from part a) to obtain a differential equation modeling the change in the catfish population with respect to time if catfish are harvested (removed) at a rate of X% of the present population per day where 0 < X < 100: (Hint X% =x/100
(d) Using that the differential equation from part b) is still logistic, determine the value of X for which in the long run, a level of 900 catfish can be sustained in the farm's lake.
Provide complete and step by step solution for the question and show calculations and use formulas.