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prisoha [69]
3 years ago
11

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

Mathematics
2 answers:
AlexFokin [52]3 years ago
8 0

Answer:

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

Eva8 [605]3 years ago
4 0

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 <em>logarithmic</em> one; every notch on the y-axis is 10 times larger than the last, so any exponential patterns will be visible as <em>lines</em> on this graph.

In a typical exponential function, you'll typically have some <em>initial value</em> and a <em>multiplier. </em>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 <em>basic reproduction number</em>, 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!

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