More on Exponential Growth

Understanding Exponential Growth

Often times exponential growth is plotted as a straight line on a semi-log plot. The Y-axis is logarithmic and the X-axis is linear. Here is an example:

What kinds of things grow exponentially?

Clearly exponential rates of growth are an integral part of the planning process. Different aspects of a growing population have different exponential growth rates and these need to be considered.

For instance, suppose your urban area is growing at the rate of 5% a year. How does this translate into the following:

Exponential Growth and Trend Extrapolation

Whenever schools get crowded, freeways get jammed, airline hubs get crowded, oil gets used up, there are no more available phone numbers, the federal debt goes beyond recovery, etc, etc is an indication of poor planning and trend extrapolation.

In a nutshell: there is no reason that we should ever be surprised at the rate of resource utilization. If we simply pay attention to past history, in general, its a fairly good guide for future resource use.

Exponential Growth and Material Exhaustion:

We are in real danger of running out of certain materials due to rapid consumption. In general, it is not cost-effective to search for new sources of these materials (e.g. it costs a lot of money to dig/mine deeper into the earth). Some examples include:

Material Rate Exhaustion Timescale
Aluminum 6.4% 2007 -- 2023
Coal 4.1% 2092 -- 2106
Cooper 4.6% 2001 -- 2020
Petroleum 3.9% 1997 -- 2017
Silver 2.7% 1989 -- 1997

The above estimates include recycling.

The difference between linear growth (constant number of units growth per year) vs exponential growth (constant percentage increase) is difficult to see initially, if the exponential growth rate is small.

We can use the Statistical Graphical Tool to help understand this.

Here is some data: