The Axis That Straightens Exponentials

You'll learnto read a semi-log plot as the field test for exponential growth.

Ten data points climb from 5 to 5,120 and the first half of them flatline into the floor of the chart. Then the y-axis takes the log treatment — and the same points snap into a perfect straight line. The semi-log plot is the field test for exponential growth, and its slope and intercept hand you the model. The trap is reading that line as linear data.

8 STEPS · 6 QUICK CHECKS · log₁₀ y = log₁₀ a + x·log₁₀ b · v3

semi-log · log₁₀ y, linear x

Before you start

What you're looking at

A vertical axis marked 10, 100, 1000 — equal spacing that means times ten, not plus a constant.

The question

On this axis, does equal visual distance mean adding or multiplying?

Watch for

The same data snapping straight once the y-axis takes the log — straight on a log axis means exponential.

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