Recall that one model for population growth states that a population grows at a rate proportional to its size.

(a) We begin with the differential equation [math]. Find an equilibrium solution:
[math]

Is this equilibrium solution stable or unstable?



Describe the long-term behavior of the solution to [math].






(b) Let's now consider a modified differential equation given by [math].

Find a stable equilibrium solution:
[math]

Find an unstable equilibrium solution:
[math]

If [math] is positive, describe the long-term behavior of the solution to [math].






Solution:

Your overall score for this problem is