Basics of Exponential Growth

Understanding Exponential Growth

Its not to great of simplification to state that the failure to understand the concept of exponential growth by planners and/or legislators, is the single biggest problem in all of Environmental Studies and/or Management.

The Two Principle Problems with Energy Management:

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:

This 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.

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:

Hey Beavis, I think we should like, uh, really know this - There might be a test on it or something

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.

If this is Internet Explorer version 4.0 then go to the Kill the Salmon applet

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