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]

[math]

Is this equilibrium solution stable or unstable?

** A. ** stable** B. ** unstable

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

** A. ** The value of [math]** B. ** The value of [math]** C. ** The value of [math]** D. ** The value of [math]** E. ** None of the above

** (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]

** A. ** The value of [math]** B. ** The value of [math]** C. ** The value of [math]** D. ** The value of [math]** E. ** None of the above

Your overall score for this problem is