Two Numbers Run the Whole Model

You'll learnto read a starting value and a growth factor out of a real exponential context.

Every exponential model is two decisions: where does it start, and what does one step multiply by? Contexts hide those two numbers behind percent language, data tables, and doubling times. Watch a, b, and the traps that come from translating them wrong — 12% loss is a factor of 0.88, not 0.12.

8 STEPS · 6 QUICK CHECKS · f(x) = a·b^x · b = 1 + r · v2

f(x) = a·b^x

Before you start

What you're looking at

A colony with 500 members at time zero and 540 a year later, beside the formula a·b^x.

The question

What must each number in the formula stand for in the situation?

Watch for

A conversion strip: 8% growth is a factor of 1.08, a 15% loss is 0.85 — a rate is not a factor.

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