Doomsday or Extinction Suppose the population model (4) is modified to be (a) If...

Doomsday or Extinction Suppose the population model (4) is modified to be

(a) If show by means of a phase portrait (see page 39) that, depending on the initial condition the mathematical model could include a doomsday scenario

(b) Solve the initial-value problem

Show that this model predicts a doomsday for the population in a finite time T.

(c) Solve the differential equation in part (b) subject to the initial condition Show that this model predicts extinction for the population as