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

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

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 , 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 , as it's usually written. represents the average number of cases of a infection person in the population is expected to spread. Novel coronavirus has an 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, 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!

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step-by-step explanation: