## 21-117: Integration and Differential Equations

# Exam #2: Review

- The Exam covers Sections 8.1, 9.1-9.5 and 17.1.

- Review Problems:
- Section 8.1: #9, 17, 21, 35.
- Section 9.1: #5, 6, 12.
- Section 9.2: #2, 7, 11.
- Section 9.3: #3, 10, 13, 31, 37, 38.
- Section 9.4: #1, 5, 13, 15.
- Section 9.5: #14. (draw the phase line for this system).
- Section 17.1: #11, 13, 21.
- Section 17.3: #2, 3, 5, 6.
- Additional Problems
- Consider the logistic growth model, modified for a constant rate of hunting:
dP/dt = .1 P ( 1 - P/1000 ) - h. If h=10, what long term predictions
does the model make? What is the minimum population that can sustain
this amount of hunting?
- Using the same model with h=30, what predictions can you make?
- The logistic model dP/dt = .1 P ( 1 - P/1000 ) can be modified to
include the effect of disease on the population. The rate of spread of
disease is proportional to the square of the population size. So we should
consider the model dP/dt = .1 P ( 1 - P/1000 ) - dP^2. How does the
carrying capacity depend on the constant d? What is the carrying capacity
if d=.01?