Chapter 4.4, Problem 4SP

Student Project: Logistic Equation with a Threshold Population An improvement to the logistic model includes a threshold population. The threshold population is defined to be the minimum population that is necessary for the species to survive. We use the variable T to represent the threshold population. A differential equation that incoqoraes both the threshold population T and carrying capacity K is

   $\frac{dP}{dt}=-rP\left(1-\frac{P}{K}\right)\left(1-\frac{P}{T}\right)$  (4.12)

where r represents the growth rate. as before.

4. This equation can be solved using the method of separation of variables. However, it is very difficult to get the solution as an explicit function oft. Using an Initial population of 18.000 elk, solve the initial-value problem and express the solution as an implicit function of t, or solve the general initial-value problem, finding a solution in terms of r. K, T. and P₀.