Today is rung 5 of 6 on this topic
Exponential growth versus linear growth
Can do: Distinguishes constant difference from constant ratio, and models exponential situations.
Why it matters
Human intuition about exponential growth is terrible, and it matters for interest, populations, epidemics and compound anything.
What it looks like when it's wobbly
Treats fast growth as steep linear growth, and dramatically underestimates the long run.
⏱️ Two-minute check
"$100 at 10% a year, or $10 added per year — which is bigger after 30 years?"
Solid looks like: The exponential, by a lot, with the reason being multiplication rather than addition.
The full activity for this topic · 25 minutes
Fold and Double
- 1Ask how thick paper would be if folded 42 times. Take their guess before calculating.
- 2Build a doubling table and watch it become absurd. It reaches the moon.
- 3Compare a linear and exponential table side by side over 30 steps.
- 4Graph both on the same axes and note where the exponential overtakes.
- 5Apply it to real compound interest or a savings plan.
If it's too hard
Doubling tables only.
If it's too easy
Exponential decay, half-life, and solving for time.
Say this
"Guess first, then calculate. Being badly wrong about this is the point of the exercise."