# Assignments: Week #7

Monday: No reading assignment in text.
Wednesday: Section 9.5.
Friday: Section 9.6.

• Exercises: Due Friday 13 October.
Section 9.1 #6ac (not part b).
Section 9.2 #12, 16, 18, 24.
Section 9.3 #40.
Section 9.4 #4, 10, 16, 21.

Additional Problems: Consider the Logistic Population Model
P' = (.1) P ( 1 - P/500 )
1. Qualitative approach:
(a) Sketch the phase line.
(b) Using information from the phase line, sketch a representative sample of solutions, including all constant solutions.
(c) Sketch the solution satisfying P(0)=100.
2. Analytic Approach:
(a) Find an explicit formula for the solution P(t) satisfying P(0)=100. (You will need to use an analytic method.)
(b) Find the limit of this solution as t approaches infinity
(c) How does this limit relate to the curves sketched in part 1(b) and (c).

• Note: Some of this weeks problems instruct you to use a "CAS". This is an acronym for "computer algebra system," a generic way of referrint to programs like Maple or Mathematica. For our purposes, though, the Java applet Dfield will suit our purposes.