Why exponential growth surprises
Growing by a share instead of an amount, and what stops it.
Linear growth adds the same amount at every step: 100, 110, 120. Exponential growth adds the same share: 100, 110, 121. For a while the two look alike.
Then they part for good. A quantity that grows by 10 % a step doubles about every seven steps, and each doubling adds as much as everything that came before it put together.
Nothing real grows like that for ever. When room or food runs short, growth slows and the curve bends into an S that levels off under a ceiling: logistic growth.
The rule of 70: a quantity growing by p % a step doubles in about 70 / p steps. At 2 % a year, prices double in about 35 years.
Early on, a logistic curve cannot be told from an exponential one. That is why forecasts of anything that spreads are so uncertain at the start.
Answer it first
A bacteria culture doubles every 20 minutes. How much larger is it after two hours?
Show the answer
64 times: two hours are six doublings, and 2⁶ = 64.
Reading is not learning it
Leo teaches this at your pace, asks for your attempt before he shows his, and checks a week later what stayed.