Math Says Yes

Concept

Exponential Growth

Quantities that grow by a constant percentage multiply rather than add, so each step is bigger than the last. The total stays deceptively flat for a long time, then erupts. Doubling is the clearest case: every step is as large as everything that came before it combined.

Lessons

A curve that starts low and then rises sharply through stacked steps.

Doubling Outruns Intuition

Repeated doubling stays small, then explodes past anything you expected.

Related Facts

A chessboard with one grain on the first square and a giant mountain of rice spilling off the far corner.

One grain of rice can bankrupt an empire

Place one grain on a chessboard's first square and double it each square — the last square alone reaches 2⁶³ grains.

A staircase of stacked coins rising slowly then steeply along an exponential curve.

Money doubles slowly, then all at once

Divide 72 by the yearly growth rate and you get the years it takes to double — a trick that hides a steep curve.