What is Exponential Growth and Why Should You Care?

Like many companies my dentist recently sent out an email outlining the steps they’re taking to keep their patients safe.  And while it was a “normal” COVID-19 related email there was one line that really struck me.  They explained that “perfect love drove their fear.”  I’ve not been able to get that line out of my head so I will open this article by explaining that perfect love drives my fear.  Perfect love also drives my motivation to write this article.

As you’ve likely heard by now… the most important thing we can do to blunt the curve of the Coronavirus Disease (COVID-19) is to practice social distancing, stay home if sick (or someone you live with is sick), and to wash our hands for at least 20 seconds on a regular basis.

The thing I want to explore in this article is the “curve” we’ve heard so much about.  This COVID-19 infection rate curve is thought to follow the exponential function which is extremely difficult for most people to wrap their minds around.  You see, most of us are guilty of something called exponential growth bias.  We tend to think things will grow in a linear – straight line – fashion.  Unfortunately, highly contagious diseases don’t work this way.

What’s especially scary is the statistics we’re reading about are probably wrong in a big way since many folks are likely sick and either don’t know it or haven’t been officially tested.  In lean and six sigma terms… there’s a high probability that our measurement system is deeply flawed.

Even still, what I hope to show here is how devastating exponential growth can be.  What I’ve done is some simple math.  I assumed 1,000 people were sick on day 1.  I also assumed a daily growth rate of 33% based on what we’re seeing in the famous Financial Times daily tracking graph (Google it).

In other words, on day 1 there were 1,000 sick people.  Then on day 2 there were 1,330 sick people (1,000 x 1.33).  And on day 3 there were 1,769 sick people (1,330 x 1.33), etc.

Now, as the graph above shows… exponential growth often lulls people to sleep early on.  By day 10 there are 13,022 sick people which is, obviously, terrible… but it’s nothing compared to day 26 when the original 1,000 sick people grows to over 1.2 million sick people.

And, what’s mind blowing is if the growth rate continues at a daily rate of 33% for 40 days in a row we’d have 67 million sick people.  I pray we never see that day.  A statistics mentor once told me, “Exponential growth is boring and small… until it isn’t.”

As another thought exercise I also ran the numbers at a daily growth rate of 25%.  This buys us a few more days.  We reach more than 1 million sick people on day 32.  But, if we’re able to knock the daily growth rate down to 5% it would take 143 consecutive days to reach 1 million sick people.

So, if you’re still wondering what all the fuss is about, and whether you should do your part in trying to blunt the growth of this wicked virus, please understand the math we’re up against.  Exponential growth is no joke.

Now, the good news is that an epidemic’s exponential curve eventually flattens out into a logistic curve once the so-called “inflection point” is reached.  But this inflection point will only occur once we’re able to reduce the growth rate.  And the other good news is we can all positively impact the growth rate by practicing social distancing (no more than 10 people being together), staying home if we’re sick, and washing our hands on a regular basis.

In closing, I want to share a quote a friend recently sent me… it read, “Your Grandparents were called to war.  You’re being call to sit on your couch.  You can do this.”

Additional Resources

Here’s an informative video about exponential growth.

3 Comments

  1. Mohamed Saleh

    March 17, 2020 - 2:23 pm
    Reply

    Extremely insightful Ron – Many thanks for sharing and making this visible – I pray we cut that curve and that we are all safe!

  2. David Acklin

    March 18, 2020 - 4:33 pm
    Reply

    Thank you Ron, the chart reminds me of the bend that is currently shaping up on the John Hopkins site. The widget “Track Reported Cases of COVID-19” is starting the turn upwards.

    https://coronavirus.jhu.edu/map.html

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