Exponentiation

Explained Visually

We seem primed to understand linear growth, but lots of processes in finance, ecology, physics and other fields depend on exponential growth.

Here's a simple visualization to help conceptualize this type of growth. It starts off {{opts.rateLabel}} with every step. Adjust the rate to see {{opts.otherRateLabels.join(' and ')}}.

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Linear growth

Most of us already have an intuition for linear growth. In the example below, each step adds a fixed amount to the total.

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Exponential growth

With exponential growth, on the other hand, each step multiplies the total by a fixed amount. So, exponentiation is repeated multiplication in the same way that linear growth is repeated addition.

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Example

The following is a naive model of the spread of a virus in a population. The number of infected individuals grows exponentially up until the virus runs out of people to infect.

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For more explanations, visit the Explained Visually project homepage.

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