Summary: Project 2: The logistic equation
Due: Tuesday, October 5
In class, we had worked with a very simple model for population growth, P (t) = kP(t). In this
project, we will investigate a more realistic model for population growth,
P (t) = kP(t) 1 -
Here, k and B are fixed, positive constants, and we will only consider values P(t) 0.
The number B is called the carrying capacity.
1. (a) Suppose at some particular time t0, P(t0) < B. Is the population increasing or decreas-
(b) Suppose that at some time t0, P(t0) > B. Is the population increasing or decreasing?
2. Find all equilibrium values for the population. (A number P0 is called an equilibrium value
if, whenever P(t0) = P0, we have P (t0) = 0.)
3. (a) Using only (1), calculate P (t). (HINT: You should be able to show that
P (t) = k2