One reason that we have an energy problem is due to exponential growth which creates a strongly non-equilbrium use of our resources. (You wouldn't know we have an energy problem if you look at traffic at 5:00 p.m.)

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:

• Failure for policy makers to understand the concept of exponential growth.
• Failure for legislation to be formulated and passed to give us a long term energy strategy

Exponential growth drives resource usage for a very simple reason:

Human population increases exponentially:

Accurate trend extrapolation is the most important part of future planning. However, failure to assume exponential growth will always lead to a disaster so always assume exponential growth when planning anything!

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

Doubling Time (D.T.) = (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:

Anytime growth depends upon a percentage on some amount that already exists we get Exponential Growth.

Exercise I. The Data Below was plotted in class using Excel Spreadsheet

Data Table

Number of Doubling Times	Amount of Stuff
0	1
1	2
2	4
3	8
4	16
5	32
6	64
7	128
8	252
9	512
10	1024

Graph of above Data:

Same Data Logarithmic Graph: Linear Relationship

Exercise II. Exponential Use: Analogy of the use of Natural Resources with Exponential Growth.

(Not totally accurate but any similarity between this analogy and reality is planned.)

• 500 unit Flask Represents Oil ( U.S. Reserves)

• Rate: Increase of consumption is 5%, 14 years doubling time.

• Start Date 1954: we used 200 units of Oil up to this time.

• Between 1954 - 1968, we used 400 units of oil. Note U.S. Reserves are decreasing. Find More Reserves: Middle East (Bigger 1000 unit Container)

• 1968 - 1982 another 800 units is used. This is more than the total 300 units used since we began using and 1968. A characteristic of Exponential Growth is: The amount used in one doubling time exceeds the total amount previously used.

• Mine oil in Alaska, mine in the North Atlantic, have a war etc. Look at what we found!!! Big Container. Lets make money!!! Keep the price down, sell it fast!! We have to have growth to survive. Keep it at 5%!! No Problem. Look How much oil we have!!

• 1982-1996: Another 1600 units is used ( Double the amount previously used) Looks like we may be running a bit low. (Is the flask half empty , half full, or just dirty.)

• How much do we need to make another 14 years? 3200 Units Again more than we used in all of history. (Pull out big container that has the stuff we have used so far). When do we think we are running out of oil??? This is a Big Container of stuff!! It looks like we have plenty but the rate of usage will use up the container that contains the same amount that we used in all of history in 14 years.

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• We would probably wake up when over half that big container is used up. Result: No more 4x4 vehicles to drive to the grocery store. That's another story.....

  • Respectfully Submitted: Stan Micklavzina