ENVS 202 On-line Access
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 Managemant.
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 desireable.
Well 10% a year may not seem inoccuous 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.
Consider this graph . The red curve is linear growth, the green curve is exponential growth. The normalization is such that at x = 1, the red curve is 10,000 times greater than the green curve. Nonetheless, by x = 15 or so the green curve has no overtaken the red curve
So it doesn't make any difference what the starting point is, exponential growth always gets out of hand.
Basic Concept of Exponential Growth
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 growth rate. Thus, if the growth rate is say 5%, the doubling time would be 14 years.
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:
