Exponential Growth Explained Simply
With linear growth, the same amount is added each time. With exponential growth, the amount is multiplied by the same factor each time - and that gets surprisingly huge, surprisingly fast.
đź’¬ Mia asks Grandpa Theo
How fast is exponential growth, really?
Look at the bacteria above: they double every 20 minutes. Starting from 1, after just 4 doublings (80 minutes) you already have 16 - and after 24 hours it would be billions!
Wow. Does that apply to money too?
Exactly, that's called compound interest: if you invest $1000 at 5% interest, you get $50 in the first year. But in the second year you get 5% on $1050, so a bit more than the first year.
Does that really add up that much?
Yes! After 10 years, your $1000 would have grown to around $1629 - just from interest continuously earning interest on itself.
$1000 at 5% interest, after 10 years: K(10) = 1000 × 1.05¹⁰ ≈ $1628.89
Check it with your calculator!
The same principle - just reversed, as a decrease instead of an increase - also explains why radioactive substances decay more and more slowly (see Radioactivity).
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