What is exponential growth?

This post will attempt to answer the following questions:

  1. What does exponential growth mean?
  2. Why is everyone so freaked out about the coronavirus when more people died of the flu this year?

Let’s say I offered you the following proposition. Would you rather I gave you;

  1. One penny on day one, two pennies on day two, four pennies on day three, and continue to double every day for 30 days or
  2. $1,000,000.

On first glance, the answer is obvious but that’s only because our brain has a hard time with exponential growth. I’ll show it to you graphically:

  1. 0.01
  2. 0.02
  3. 0.04
  4. 0.08
  5. 0.16
  6. 032
  7. 0.64
  8. 1.28
  9. 2.56
  10. 5.12
  11. 10.24
  12. 20.48
  13. 40.96
  14. 81.92
  15. 163.84
  16. 327.68
  17. 655.36
  18. 1,310.72
  19. 2,621.44
  20. 5,242.88
  21. 10,485.76
  22. 20,971.52
  23. 41,943.04
  24. 83,886.08
  25. 167,772.16
  26. 335,544.32
  27. 671,088.64
  28. 1,341,177.28
  29. 2,684,354.56
  30. 5,368,709.12

So, if you chose the million you chose poorly and would have lost over $4million – ouch. What’s interesting about the exercise is that if you were to stop the tape half way through, you would be feeling pretty good about yourself. The penny guy has a few hundred bucks and it’s looking grim while you are planning on how to spend your cool million. But then things change and they accelerate quickly. By the last few days you will see how poor your choice was. This is exponential growth. Its when the growth rate accelerates with time.

This is exponential growth. Its when the growth rate accelerates with time.

Now imagine you are working at the CDC or WHO and you see that the number of cases is doubling every few days and starting on a path towards exponential growth. You know the formula for exponential growth so you sound the alarm. Now imagine what the world might say on day 8 or 10 when there are only a few hundred or a few thousand cases. You would hear friends, families, media pundits, and politicians say things like, ‘its not so bad, there are only a few thousand cases’ or ‘this is all a hoax designed by [insert hated group here] to cause [insert nefarious gain here].

On of the most common misplaced comparison that has been circulating is between seasonal flu and COVID-19. The root of this logical fallacy is that, thus far in the United States, far more people have been infected with and have died from seasonal flu than from COVID-19. Its an erroneous comparison for multiple reasons but the one I’ll focus on is based on the problem of exponential growth. Flu is not growing exponentially, COVID-19 is. Flu is relatively static. Its like choosing the million dollars. While we ar early on flu will look like the million dollar choice and will have numbers far greater than than the penny doubling choice. But, as you can see from the last quarter of the list, things ramp up quickly and can get out of hand fast. This will then overwhelm hospitals and society as a whole before anyone realizes what’s happening.

Flu is not growing exponentially, COVID-19 is.

Early modeling predicted that, if nothing was done, 88% of the population would be infected with COVID-19. As of 2018 the population of the United States was 327,000,000 which means that about 288,000,000 people would be infected. This means that even if we took the lower end of the mortality estimate (~1%) and cut it in half that would mean that about 1,500,000 people would die. This would also completely destroy our healthcare system.

That’s why governments have been shutting things down long before the number of cases is so high. The health departments and CDC were seeing the growth start to go exponential and were trying to stop it before it got out of hand. If they waited until it killed more people than flu it would be too late with catastrophic results.

For a clear explanation of how exponential growth relates to tracking the progress of COVID 19, check out this youtube video.

4 thoughts on “What is exponential growth?

  1. Exponential growth is the idea behind chain letters and Ponzi schemes. These fail because eventually, you run out of gullible people. This happens fast now on those two things because there were enough of them to teach us all.

    Any living thing that finds a new food source goes into exponential growth, also called the log phase of an S-shaped curve. Log for logarithmic growth. Drawn on special “logarithmic graph paper,” the curve looks like this:
    The time-axis of this graph is linear. Each quarter-inch (or each cm) might be another hour or another day. But the other axis has the same heishe for a doubling or a ten-fold increase. Websearch “S-shaped curve” and “logarithmic graph” and you can see what these look like.

    A disease goes into log phase or exponential growth before you even hear about it, usually. Eventually, they run out of susceptible hosts, and then it may die off completely.
    Coronaviruses, also known as colds and flu, have a seasonal pattern. They normally die off in the Spring when people get out into the sunshine and make more vitamin D. Quarantining has at least doubled the deaths so far from COVID 19, and will be 10X to 1000X before people wake up to it. If we are lucky, a few countries will refuse this unlawful quarantine. Those will “fall off” the usual curve shown by Dr. Groves. Eventually, the rest of us will “get it,” and know that quarantining can be a very bad idea (it can also work well when done right).
    A hundred years ago, we knew that respiratory diseases need fresh air and sunshine. When we recover that knowledge, life expectancy will rise and we may even make up for the tragedy of this quarantine.

    Like

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