MathBench > Population Dynamics

Mystery of the Missing Housefly

You write the equation

I prefer action to words, and I prefer words to numbers, and I prefer just about anything to formulas, but the two century notes she laid on my desk were having the desired effect.

If I was going to crack this case, I'd have to use my head for something other than a battering ram. Just how many of Ms. Domestica's relatives were missing, and how much insurance money did that add up too?

 

 

OK, lets give it a try. I'm going to pick some small numbers, so as not to overwhelm your calculator. Let's say you start with 3 flies, and each fly lays 2 eggs at a time, which take 1 month to mature. After 1 month, all of the new flies lay eggs and die on the spot.

Your assignments are:

  1. write an equation for this process,
  2. write the initial condition
  3. iterate the equation for 12 months (use a calculator!), and
  4. graph the population dynamics

In case you need some hints:

  1. To write an equation, think about how fliest (number of flies at time t)
    relates to flies t-1 (number of flies the month before).
  2. The initial condition is simply how many flies there are at the Beginning of Time (flies0)
  3. To iterate your equation, start at time 0 and work forward for 10 months,
    making a table with months and flies as headings
  4. To graph the dynamics, just graph the table of numbers you created in the third step.