Equal Amounts, Equal Factors

You'll learnto hear whether a table is linear or exponential from what happens between its rows.

A linear function and an exponential function both climb — by different laws. One adds the same amount over every equal input interval; the other multiplies by the same factor. Learn to hear which law a table is speaking, read a and b without garbling them, and watch the line’s head start evaporate.

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

equal amounts vs equal factors

Before you start

What you're looking at

A linear table and an exponential table side by side, with subtraction arrows and division arrows between the entries.

The question

Between equal input steps, is the output changing by a fixed amount or a fixed factor?

Watch for

Subtraction reveals a line; division reveals an exponential — two different questions.

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