# 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 flies
_{t}(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 (flies
_{t=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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