Problem Set #2
All three exercises are from Module 2.3 on p. 40.
- Exercise 3 (I apologize for the use of Imperial units.)
- Exercise 4 In the past I've skipped this problem because of the amount of math invovled, but considering how
many of you are interested in medicine, I wanted us to take a stab at it this time.
As usual, when you see “solve using calculus”, you have two choices:
- Do like I do, and google it. I found a several solutions
by googling GOMPERTZ EQUATION, which requires you to translate the between textbook's variables
(N, M, k) and the ones in the solution (y, K, r),
something you often have to do it situations like this. Even then, it's nontrivial, so here is
one weird trick you can use.
- Be a calculus hero and solve it with your skillz, for
teh extra creditz.
- Exercise 5 I would use Excel to produce the graph (part a): Enter the numbers 0 through 10 in Column A, then in cell B1 type the formula = EXP(-A1), and copy-and-paste into the remaining cells in column B. Then do Insert/Scatter and choose the smooth-line plot. Then copy-and-paste the plot into your writeup. For 5b-f, Excel and Vensim can also help you to match the formulas (A-F) with the English descriptions (b-f),but all you need to turn in for these is the final answer (what goes with what).