Question

What is a real-world example of an exponential function?

Answer 1

Answer:

Population growth, radioactive decay, and loan interest rates, calculate half-life, or plan your budget.

Answer 2

Disease spread is modeled with exponential functions very frequently, at least in the early stages of growth. For a particularly relevant example, I've attached a graph tracking the growth of the novel coronavirus, through its outbreak in several major countries. Note that this graph is a logarithmic one; every notch on the y-axis is 10 times larger than the last, so any exponential patterns will be visible as lines on this graph.

In a typical exponential function, you'll typically have some initial value and a multiplier. For example, in the function $f(x)=3\cdot2^x$, we start with an initial value of 3 and double that value every time x is incremented by 1. Epidemiologists have a special name for the multiplier in the case of a disease or potential epidemic: the basic reproduction number, or $R_0$, as it's usually written. $R_0$ represents the average number of cases of a infection person in the population is expected to spread. Novel coronavirus has an $R_0$ between 2.1-2.7, meaning the average carrier will spread it to at least 2 other people over the course of their infection. This seems like a small number at first, but doubling the number of infected each period leads to some frightening growth.

Thankfully, $R_0$ isn't the only thing that matters for the spread of disease, as in many cases it doesn't take into account preventative measures taken against spreading infection. Sheltering-in-place, social distancing, and effective hygiene go a long way, and you should be practicing them as much as you can in these coming weeks and months to help turn this exponential curve into a linear one!