Q3. If a constant number h of fish are harvested from a fishery per unit time, then a model for the population o P(t) of the fishery at a time t is given by dP = P(a – bP) – h, P(0) = Po, || dt where...

please explain all steps, show detailed solutions and more explanation for part b. please do not take from others

Extracted text: Q3. If a constant number h of fish are harvested from a fishery per unit time, then a model for the population o P(t) of the fishery at a time t is given by dP = P(a – bP) – h, P(0) = Po, || dt where a, b, h, and Po are positive constants. i) Solve this IVP, provided that a = 5, b = 1 and h = 4. ii) Suppose a = 5,6 = 1 and h = 4. Then Use part (i) to determine the long term behavior of the population for the cases 0 < po="">< 1,="" 1="">< po="">< 4,="" and="" po=""> 4. iii) Use the information in parts (i) and (ii) to determine whether the fishery population becomes extinct in finite time T. If so, find that time T.