a differential equivalent problem
3. There is considerable evidence to support the theory that for some species there is a minimum population m such that the species will become extinct if the size of the population falls below m. This can be incorporated into the logistic differential equation by introducing the factor (1-m/P). Thus, in this case we model the size of the population by the differential equation dt where r >0 and K>m >0 are constants. (a) Find the equilibrium solutions for (t). Using interval notation, give the values of P for which the solutions for the population P(t) are strictly increasing. For which values of P are the solutions P(t) strictly decreasing? Finally, giving justifications, classify the equilibrium solutions. Summarize your results in a phase line diagram. 12 (b) At what value of P does P() grow fastest? Justify your answer. MATH2305 continued