Consider a population model, with population function P(t), where we as- sume that : the number of births per unit of time is P(t), Where ,8 > O; the number of natural deaths per unit of time is 5P2 (t), Where 5 > 0 ; the population is subject to an intense harvest : the number of deaths due to harvest per unit of time is wP3(t), where w > 0. Given these informations, 1. Give the differential equation that constraints P(t) ; 2. Assume that P(0) = P0 2 0. Depending on P0, ,8, 5 and P0 : (a) When does P(t) > 0 as t > +00 ? (b) When does P(t) converge to a nite strictly positive value as t > +oo ? What are the possible limit values ? (c) If we decrease to a little bit, What happens to the critical points