Exponential growth is a matter of math

By Murray Siegel

Recently, I saw a relevant cartoon based on most Americans not having a mastery of mathematics. It was set in a high school algebra classroom, with the teacher delivering a lesson on exponential growth. One student asks another, “When will we ever use this?”

Today, we hear about the exponential growth of the COVID-19 virus.

What does exponential growth mean and why is it meaningful in dealing with the pandemic? An exponential growth model means the percentage change in the growth is constant, while a linear growth model has a constant change. This difference can be best understood by investigating a financial situation.

An amount of $1,000 is invested at a 6% annual rate, and there are two options. One option provides a constant amount of interest each month of $5 – the monthly interest is one-twelfth of the 6%, 0.005 X $1,000 = $5. After 30 years, this investment is worth $2,800, this is linear growth. In the other option, each month the interest is 0.005 times the balance in the account, which grows monthly. At the end of 30 years, this investment is worth $6,022.58. This is the explosive power of exponential growth.

If the virus infections increase at a constant percentage, the number of new infections each day will be greater than the previous day, and our healthcare system will be overwhelmed. There is only one means to stop the exponential growth, and that is to limit the number of potential victims who are exposed. The lockdown rule accomplished that by limiting contact between infected and uninfected. Unfortunately, this method has serious negative emotional and financial consequences.

A second way to limit the exponential spread is a successful vaccine, yet it could take another year or more to approve one that is safe and effective. Dr. Anthony Fauci keeps talking about the need for a randomized controlled study of a potential vaccine with the use of a placebo. Most Americans do not understand what this means and why it will take so long to develop a vaccine. Randomized studies and the placebo will be discussed in this column next month.

The third way to stop the spread is to expose most of the population so there are very few uninfected people. If the consequence of COVID-19 was a bad cold and a few days of fatigue, this “crowd immunity” could be effective. Unfortunately, COVID-19 kills, and sacrificing a few million people so we can crank up the economy is unethical. So, understanding exponential growth and how to limit that growth is a lesson all Americans must understand.

No student in math class should ever ask when will this knowledge be useful.

Murray Siegel, Ph.D., has 44 years of experience teaching mathematics. He is a volunteer at Butterfield Elementary School.

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This column appears in the June issue of InMaricopa.