It’s Exponential! So What?

Survival Math and the New Normal
Palm Beach Daily News: Opinion

This was originally published in my hometown paper, the Gainesville Sun and then picked up by the palm Beach post.

Which would you choose: a million dollars upfront or one penny that doubles every hour for the next two days? Not sure? We will revisit this question. First, let’s examine how to think mathematically about an exponential increase.

Lots of things all around us every day are increasing exponentially. The bacteria on that kitchen counter you forgot to clean are doubling every 20 minutes. The human population that you are a member of has been increasing exponentially for thousands of years.

In 1804 the first billion people appeared on Earth, double the 500 million found 200 years before. It took about 120 years to double to 2 billion in 1927, and a little under 50 years to become 4 billion-plus in 1974. Today, just over 35 years later, there are almost 7.8 billion people on the planet.

Human exponential increase is slower than bacterial growth because our reproductive life span, averaging around 27 years, is much longer. The bacteria on your counters will have doubled soon after you finish this article. There are millions of them. You really should clean that counter.

Meanwhile, if you chose the penny, you will soon have 2 cents. So exponential increase involves something that doubles or more than doubles at regular intervals.

Another exponential increase we are watching right now is the coronavirus SARS-COV-2 infections. A virus reproduces differently from those bacteria happily dividing away on your counter-top. Bacteria consist of single cells with all the machinery needed to make new cells on their own. A virus, on the other hand, depends on other living things to reproduce.

Viruses are just genetic material wrapped in a fat and protein coat. SARS-COV-2 has a single strand of RNA similar to but different from our DNA. They have to inject that RNA into a living cell and then hijack its machinery to produce more viruses. Viruses are not technically a living organism since they cannot reproduce independently.Y

SARS-COV-2 depends specifically on human cells to reproduce. It takes human-to-human contact of some kind to spread the infection. Scientists know from brief experience with this 6-month-old virus that limiting human-to-human connection will starve SARS-COV-2 and prevent it from reproducing. Staying at home, social distancing and wearing masks all help prevent the disease from finding new hosts so they can reproduce.

And just like those millions of bacteria reproducing on your kitchen counter, viruses are killed easily with soap and water. Washing your hands and cleaning kills most of them. This is even more effective if you use a disinfectant like bleach, peroxide or Lysol.

The bacteria in your kitchen are entering the end stage of exponential increase, where it becomes evident that we have a problem. One microscopic bacterium is not much of a threat, but in a week of exponential growth, that one bacterium can become billions. Those billions give your counter an unhealthy sheen and produce a funky smell. It’s not a good time for company.

Because they begin small and accelerate at the end, exponential scenarios are sneaky. Back in February, the people who can think mathematically actually saw the corona crisis coming. They went out and bought up all the toilet paper.

As we watched China and Italy go through their medical emergencies, people who understood exponential increase knew that only one, or only 15 cases in the United States, were going to become millions. They stocked up and isolated before official lock-down orders came.

Their efforts helped their families survive, protected their friends and neighbors, and kept their local medical facilities from becoming overrun. A little mathematical thinking can increase in value exponentially. (Math joke!)

Let’s return to the penny. If you took the million dollars, you could afford to go out and buy some antiseptic cleaner for your kitchen counter if you can find any. (I can’t!). But if you are only worth 2 cents right now, but wait.

By tomorrow morning, you will have $40, enough to buy some cleaner. By evening you will have over $2,000. By the second day, you have over $160,000, and at the end of two days, you will be worth $2,814,749,767,106.56 — or almost $3 trillion.

Remember, you made most of that in the last couple of hours as astronomical sums kept doubling. Exponential thinking can pay off in many ways.

Keep safe, starve the virus and think mathematically!

Mary Bahr lives in Gainesville and taught science in public schools for 20 years.