# Reading and Homework: Week #6

Monday: Snow Day!
Wednesday: Section 5.2 and 5.3.
Friday: Section 5.4.

• Exercises: Due at the start of class on Friday 21 February.
#4.3.1, 4.3.4, 5.1.1, 5.1.2, 5.1.3, 5.1.4.
#4.2.2, 4.2.9, 4.2.10, 4.3.11, 5.1.5.
#4.2.3.

Recall that we derived the Logistic Population Model in class: P'=kP(1-P/M)

1. Modify the Logistic Model to account for hunting at a rate proportional to the size of the population.

2. What are the equilibrium solutions for your modified model? How many are there? Does the number depend on the value of the proportionality constant you chose in #1?

3. Draw the phase line for your differential equation in the case where the proportionality constant is relatively small. Use the phase line to sketch some solutions. (Try to select a representative sample of solution curves.)

Notes:

1. For problems in Section 4.3, when you are asked to sketch solutions, first draw the phase line for the equation, and use that as a basis for sketching the solutions.

2. Problems 5.1.1, 5.2.2 and 5.2.3 are written in a stupid way. Or at least an unhelpful way. Each "system of units" is based on three basic units, one for length, mass and time. All other units are derived from these units. So, for example, in the mks system,

[Force]=[mass]x[acceleration]

or

[N]=[kg]x[m/s^2]

So a Newton is a (kg m)/s^2. The other thing they neglect to tell you is that weight is a force, not a mass. The reason these problems (5.1.1 anyway) are necessary is that in everyday usage we, users of the British system, confuse weight and mass. We think of pounds as both weight and mass, and no one has ever heard of a slug. It's just a charming part of our culture.