Exponentiation

By Victor Powell

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 doubling with every step. Adjust the rate to see tripling and quadrupling.

steps: 4 speed: 5

12

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.

steps: 10 speed: 10
+1+1+1+1+1+1+1+1+1+1

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.

steps: 4 speed: 10
x2x2x2x2

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.

speed: 8 people infected over time

For more explanations, visit the Explained Visually project homepage.

Or subscribe to our mailing list.