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  • About 70 min
  • 9 steps · 2 quizzes

Exponential Growth — Why Doubling Surprises Us

A hands-on, 45-minute lesson on exponential growth: what makes doubling different from adding, why it fools our intuition, and where it shows up…

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9 steps · 2 quizzes · about 70 minutes · open any step

  1. Fold a paper to the MoonStart hereA sheet of paper is about 0.1 mm thick. Fold it in half and the stack is twice as thick. Fold again: twice as thick again. Try it: type your guess first, then fold.InteractiveHands-on · 6 min
  2. Adding vs doublingTwo ways to grow: - Linear: add the same amount each step (+100, +100, +100…). - Exponential: multiply by the same amount each step (×2, ×2, ×2…). Try it: which plan would you pick for a month? Press Play to day 30.InteractiveHands-on · 6 min
  3. The rice on the chessboardAn old story: an inventor asks a king for one grain of rice on the first square of a chessboard, two on the second, four on the third — doubling across all 64 squares. The king laughs at such a small reward. Try it: fill the first row, then the whole board.InteractiveHands-on · 6 min
  4. How long to double? The rule of 70Anything that grows by the same percentage every year doubles in the same number of years, again and again. A quick way to estimate that time: Doubling time ≈ 70 ÷ the growth rate in % · Try it: drag the growth rate and compare the rule with the exact answer.InteractiveHands-on · 6 min
  5. Check: doublingQuiz · 4 questions
  6. Money that grows on itself: compound interestPut money in a savings account at 7% a year: - Simple interest: you earn 7% of the starting amount, every year. - Compound interest: each year's interest is added in, so next year you also earn interest on the interest.InteractiveHands-on · 6 min
  7. Growth meets its limitsNothing can double forever. Bacteria run out of food, a viral post runs out of new people to reach, an app runs out of new users. Growth slows and levels off in an S-curve. Try it: press Play. Then switch on Unlimited room and food and play again.InteractiveHands-on · 6 min
  8. Shrinking by half: exponential decayExponential change can go down as well as up. In exponential decay the amount halves every fixed stretch of time: its half-life. Your body clears caffeine roughly this way. Try it: halve the jar a few times. Then choose when you drink your coffee.InteractiveHands-on · 6 min
  9. Seeing growth clearly: the log scaleOn a normal chart, exponential growth hides near zero and then shoots off the top. A log scale fixes this: each step up the axis is ×10 instead of +10. Try it: switch between the two scales, then drag the blue line's growth rate.InteractiveHands-on · 6 min
  10. The lily pond: why doubling surprises usLily pads on a pond double every day. On day 30 the pond is completely covered. Try it: answer the question first, then press Play.InteractiveHands-on · 6 min

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