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Comment by FartyMcFarter | Hacker News Reader

Most people don't think of 2% annual growth as exponential.

“Most people” could not accurately define the word “exponential” even if they were offered an exponential amount of money every year to do so.

To be fair they'd be incentiviced not to... assuming they understand the exponential nature of the money, which I guess they don't. But as soon as they do learn they won't want to explain.

Also, growth narrative is always about adding/subtracting percent points - which makes most people think this is a linear phenomenon, because they don't make the connection that the quantity discussed is a multiplier, and charts they see are on log scale.

As long as you stay with low percentages, the linear approximation works pretty well: two times 1% lead to a 2.01% increase. But it starts breaking down as soon as you reach 10%.

Little trick to know (with some good approximation) the doubling time of some low-percentage growing system: count it linearly up to 10% and then multiply by 7 (which is roughly the doubling time for 10% growth). Example: 2% => 5*7=35 years to double.

This is identical to the Rule of 72, https://en.m.wikipedia.org/wiki/Rule_of_72. Except that you are using 70. The amazing thing about the rule of 72 is that it works pretty well even for rates greater than 10%.

Or, in this context, 20% daily growth of coronavirus cases -> 20% => 0.5*7 = 3.5 days to double.

And even fewer realize that a 2.1% growth rate is itself exponentially faster than a 2% growth rate.

If something grows by 2% per day, vs 2.1% per day, after a year the second one is >20x bigger.

What you say is true in principle, but your numbers are wrong. I got a rather less dramatic 50% difference after a year:

  >>> 1.02**365
  1377.4082919660768
  >>> 1.021**365
  1969.6808462403098
  >>>

Thanks for the correction, I didn't actually do the math for that, just remembered something I've read a while back, but the numbers where different 20% vs 21%.

Apparently I don't understand exponential growth either cause I assumed a 5% difference scales linearly (as in the difference between 20% vs 21% growth rates for a given period should be the same as between 2% and 2.1%).

Silly me.

But a good exmple showing why numbers are so important. A 50% difference is an order of magnitude away from a factor 20. Thing is, once out there the wrong factor 20 is impossible to correct.

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