Most people don’t understand exponential growth. It can be counterintuitive and is easily misinterpreted. Understanding it is particularly important right now around Covid-19.
The following eight-minute video is extremely well done and uses the historical Covid-19 data to help understand exponential growth.
There’s a magic number in this that we should be focusing on, but gets lost in the fog of hysteria. The math lesson starts at about 3:45.
The magic number is the growth factor, which is the change in new cases today divided by the change in new cases yesterday.
Right now we have a growth factor > 1, which is the fast-growing part of the exponential curve (the scary green part.) When the growth factor is < 1, we are on the slowing down part of the curve (red). We hit an inflection point when the growth factor = 1, which means that we are transitioning from rapid growth to slowing growth.
However, since we are dealing with the rate of change of new cases on a daily basis, the absolute number of cases obscures what is going on.
Look at the following table. The absolute number of change is scary, but if the growth factor hits 1, things are getting better.
Compare that to when the growth is 1.15 (15%). Note that the difference in the absolute numbers are not that significant, but the implication is dramatic.
When the growth factor is > 1, there may be orders of magnitude more growth ahead of us. When the growth factor is < 1, the most things with grow from there is 2x.
In addition, the growth rate from here has a huge outcome on number of cases. For example, if we are at a 15% growth rate from here (21,000 cases), in 61 days of 15% daily growth, we’ll be at over 100 million cases. But, if the growth rate decreases to 5% (a growth rate of 1.05, which is still > 1), in 61 days we’ll be at slightly over 400,000 cases.
The growth rate matters a huge amount right now. The more we can do to slow the growth rate, the better things will turn out. And, this activity is exponential, not linear, so massive change right now has an enormous impact on things.
If you want to track these numbers, the best three sites on the web that I’ve found that have these data and explanations organized are Our World in Data, Worldometer, and the Johns Hopkins Covid-19 site.