Basics of Exponential Growth

Understanding Exponential Growth

Exponential growth drives resource usage for a very simple reason:

Human population increases exponentially:

At the moment there seems to be very little that can be done about this and hence, this represents our fundamental problem. That is, you can't really stop it, only slow it down and plan accordingly.

Intelligent planning for exponential resource usage is directly related to environmental problem solving as follows:

Now, of course, the problem is made worse by the perception that we are all afraid of math and that "formulas" don't apply to real life.

"Math, formulas and other things that don't apply to real life"

(--anonymous comment from student evaluation of Physics 161 course as the part they liked least about the course)

So we live in a society that is afraid of and doesn't understand numbers.

This again is a recipe for disaster as it means the public can be sold most anything

An example:

A survey of Boulder Colorado residents about the optimal size for growth returned a result that most residents thought that a growth in population at the rate of 10% per year was desirable.

Well 10% a year may not seem innocuous but let's see how these numbers would add up?

So in 7 years (year 2--7) the population has doubled and by then 10,000 new residents per year are moving to Boulder!

Clearly, Exponential growth, in general, is not understood by the lay public. If exponential use of a resource is not accounted for in planning - disaster can happen.

The difference between linear growth and exponential growth is astonishing.

In this example, one can clearly see that no matter what the growth rate is, exponential growth stars out being in a period of slow growth and then quickly changes over to rapid growth with a characteristic doubling time of

70/n years; n =% growth rate

Its important to recognize that even in the slow growth period, the use of the resource is exponential. If you fail to realize that, you will run out of the resource pretty fast:

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.

Exponential growth means that some quantity grows by a fixed percentage rate from one year to the next. A handy formula for calculating the doubling time for exponential growth is:

Doubling Time = 70/n years

where n is the percentage growth rate. Thus, if the growth rate is say 5%, the doubling time would be 14 years.

Try the Salmon Sustainability Applet

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