First, a more detailed look at OHM's Law and Circuits (see also Chapter 9 in the book)

Exponential Growth and Resource Usage

Go Here for Stan's Stuff

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.

Its not too 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 Resource Management.

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?

• Year 1 60,000
• Year 2 66,000
• year 3 72,600
• Year 4 79860
• Year 5 87846
• Year 6 96630
• year 7 106294
• Year 8 116923

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

The difference between linear growth and exponential growth is astonishing.

Consider the graph above. The red curve is linear growth, the green curve is exponential growth. The x-axis is in years and the Y-axis is in relative units of resources being used. The normalization is such that at x = 1 year, the red curve is 10,000 times greater than the green curve (and so the green points are not plotted). Let's say that when 200 units a year of the resource is being used, it will quickly run out. For the linear case, we can see that it would take 90 years to reach this usage rate. For the green curve, even though the initial point was 10,000 times smaller, 200 units a year or being used by year 17 and the usage skyrockets after that!

So it doesn't make any difference what the starting point is, exponential growth always gets out of hand.

Basic Concepts 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 important example

What kinds of things grow exponentially?

• Population
• Energy resource use
• Number of shopping malls
• Number of automobiles on the freeway
• Your tuition (up to a limit)
• Number of Xerox Machines
• Number of cows McDonalds uses each year
• Number of hospital patients
• Number of prisoners
• Number of Web Pages

  any resource that people use will grow exponentially

  

  Previous Lecture Next Lecture Course Page