1.3 Exponential Growth

 

Figure 1.3.1 Mathematical Representation of Exponential Growth:[see reference 3]

Figure 1.3.1 sourced from Wikipedia (Author: McSush) under a the Creative Commons CC0 1.0 Universal Public Domain Dedication License
http://en.wikipedia.org/wiki/File:Exponential.svg

The above graph shows three different functions increasing over time. The y axis is the amount of something; the x axis is increasing time. The red graph increases proportionally, the blue increases cubically, and the green graph increases exponentially. In this example the exponential graph doubles over a set period of time but it could triple, quadruple or increase by any factor of x over time.

The green graph is the important one as it is this model that many world systems such as population growth and resource consumptions follow. The shape of that graph and the concepts it introduces are essential to understanding the trajectory of patterns in society.

Example: A bacteria is introduced to a lake of a finite size. The bacteria cover a set area of the surface of the lake, and this area doubles in size every hour. After 1 hour the bacteria covers 1% of the lake. How many hours will it take to cover the whole lake?

It takes 6 hours for the bacteria to cover just under one third of the lake (32%), but in the next hour and a half, it covers the whole of the lake. This example is intended to demonstrate the nature of exponential growth – amounts become very large very quickly.

It could be considered that we are now in that final hour, where the amount of water left on the lake is our remaining resources. If it is known that the world is strained with our presence currently, those strains will double in a short period of time, and double again after that unless radical changes are made.