Assume we are considering the survival of whales and that if the number of whales falls below a minimum survival level m, the species will become extinct. Assume also that the population is limited by the carrying capacity M of the environment. That is, if the whale population is above M, then it will experience a decline because the environment cannot sustain that high a population level. Q1. Discuss the following model for the whale population dP dt = k(M-P)(P-m) Where P(t) denotes the whales population at time t and k is a positive proportionality constant.
Q2. Graph dP/dt versus P and P versus t. Consider the cases in which the initial population P(0-Po satisfies P)