# ...and an equation

I poured myself a stiff one, to clear my head. The numbers were crashing into each other like a county fair demolition derby, but the answer was still coming out the same. “And…” I said. |

Let's look at the equations in a little more detail:

flies, which simplifies (using algebra only) to_{t}= 120* flies_{t-1}- .99 * 120 * flies_{t-1}

flies, and doing some math I get_{t}= (120 - .99 * 120)* flies_{t-1}

flies_{t}=1.2* flies_{t-1}

So, I can simplify the growth-and-death equation into something that looks a lot like an exponential growth equation -- in fact, it *is* exponential growth. In both cases, the number of flies in a certain month equals the number of flies the month before multiplied by some constant number.

So we can say that these two models have the same **functional form **, and therefore the same shape on a graph. The form is

flies_{t}=r * flies_{t-1}

where r is the "rate of growth", taking mortality into account.

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