Chapter 4.2, Problem 27E

Logistic Growth Animal populations are not capable of unrestricted growth becomes of limited habitat and food supplies. Under such conditions the population follows a logistic growth model:

$P\left(t\right)=\frac{d}{1+k{e}^{-ct}}$

where c, d, and k are positive constants. For a certain fish population is a small pond $d=1200,k=11,c=0.2,$ and t is measured in years. The fish were introduced into the pond at time $t=0.$

(a) How many fish were originally put in the pond?

(b) Find the population after 10, 20, and 30 years.

(c) Evaluate $P\left(t\right)$ for large values of t. What value does the population approach as $t\to \infty ?$ Does the graph show confirm your calculations?