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 to?
OK, let's 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:
- write an equation for this process,
- write the initial condition
- iterate the equation for 12 months (use a calculator!), and
- graph the population dynamics
In case you need some hints:
- 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).
- The initial condition is simply how many flies there are at the Beginning of Time (fliest=1)
- To iterate your equation, start at time 0 and work forward for 12 months,
making a table with months and flies as headings
- To graph the dynamics, just graph the table of numbers you created in the third step.
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