What is exponential growth?

Exponential growth happens when a quantity grows in proportion to its own size. Each period it adds the same percentage, so the absolute increase gets larger each time. It matters because it starts slowly, then becomes explosive, which makes it easy to underestimate and hard to manage once it takes off.

How it works

The cause is a reinforcing feedback loop: more of the quantity produces more growth, which produces more of the quantity. Examples are compound interest, early viral spread, and a startup growing by word of mouth. A handy shortcut is the doubling time, which is about 70 divided by the percentage growth rate per period. At 7 percent per period, the quantity doubles about every 10 periods.

Pure exponential growth does not last, because real systems have limits. Sooner or later a balancing force appears, such as a market running out of new customers, and the curve bends into S-shaped growth, or it may overshoot and collapse. When you see rapid growth, ask what will limit it and when. See also limits to growth.

Example

Say a community has 1,000 members and grows by 10 percent a month. After one month it has 1,100, after two 1,210, after three 1,331. The monthly gain rises from 100 to 121 to 133. After 12 months it has about 3,138 members, and after 24 months about 9,850. The doubling time is about 7 months. This is an illustration with round numbers.

How to model it in Machinations

Use a Pool for the quantity, a Source that feeds it, and a state connection from the Pool to the Source so that the rate is a percentage of the Pool. Put the percentage in a Register. Play and chart the Pool, then move the percentage with a Lever to see how small changes in the rate produce large changes in the end value.