Chapter 4.4, Problem 3SP

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.

3. What is the limiting population for each initial population you chose in step 2? (Hint: use the slope field to see what happens for various Initial populations. i.e., look for the horizontal asymptotes of your solutions.)