← ELI5 · Nestor G Pestelos Jr

Mathematics

What is exponential decay?

It's when something shrinks by a percentage of itself each step, instead of by the same fixed amount every time, so the smaller it gets, the smaller each step's loss gets too.

Losing a percentage, not a fixed amount

Six bars, each exactly half the height of the one before: 128, 64, 32, 16, 8, and 4 128 64 32 16 8 4 −64 this step −4

Going from 128 to 64 loses sixty-four. Going from 8 to 4 loses only four. Same halving rule, much smaller loss, because it's applied to a much smaller number.

Half of what's left, every half-life

A tank that drains as a substance loses half of what remains each half-life; a slider moves through zero to ten half-lives 4 half-lives 6.3% left

Using carbon-14's real half-life of 5,730 years: 22,920 years have passed at this point.

It never quite hits zero

A curve that keeps dropping and flattening but never reaches the zero line, crossing a dashed detector noise floor partway across, after which the real signal can no longer be told apart from noise detector noise floor signal lost here

The curve keeps shrinking forever, in theory. In practice, once what's left drops below what an instrument can detect (for carbon dating, that's around ten half-lives), there's no way to tell the real signal apart from noise.

Sources: "21.3 Radioactive Decay," Chemistry 2e, OpenStax. "Radiocarbon Dating," Chemistry LibreTexts. Longer, more technical version: Reference: Exponential Decay.

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