# MathBench>Population Dynamics

## Mystery of the Missing Housefly

 “You've been playing me for a sap!” I growled. “No, no," she buzzed. “What makes you think such a thing?” “Listen, sister,” I said, turning my back to her, but keeping an eye on her through the reflection of my office window. “Either spill the beans, or walk out the door right now. Although your two C-notes are welcome to stay.” “Oh, all right,” she wept. “I should have known I couldn't keep it all from you. The truth is, they, they didn't all survive.”

Our exponential model made a number of assumptions , two of which are:

• 1. all offspring survive long enough to reproduce
• 2. all flies have the same number of offspring

When you evaluate a model, one thing to think about is the assumptions of the model. Are they reasonable? Would a different assumption give you a different outcome?

Let's start with the assumption “all offspring survive”. That's obviously pretty unrealistic. Most fly offspring die as eggs or larvae or sometime before they could reproduce. This would be a violation of the assumption that all flies survive. (In case you're wondering, maggots need sufficient warmth, moisture, and food, and full-grown flies fall prey to birds, reptiles, and window sills.)

So let's set up a new model, where 99% of the flies die before they have a chance to reproduce. Here's the old model equation:

flies t = 120* flies t-1

See if you can come up with an equation that describes each fly laying 120 eggs, but 99% dying.