Chapter 4.2, Problem 27E

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

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

where c, d, and k are positive constants. For a certain fish population in 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.

1. (a) How many fish were originally put in the pond?
2. (b) Find the population after 10, 20, and 30 years.
3. (c) Evaluate P(t) for large values of t. What value does the population approach as t → ∞? Does the graph shown confirm your calculations?