Trend Extrapolation

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Exponential Growth and Trend Extrapolation

Accurate trend extrapolation is the most important part of future planning. As we shall see from some real examples below, this is not often easy.

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, expoential 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

Now do another applet on Greenhouse effect

The Internet is growing, for instance, at a horrific rate. This of course, is why, like it or not, it will impact everyone's life.

In a nutshell: there is no reason that we should ever be surprised at the rate of resource utilization. If we simply pay attention to past history, in general, its a fairly good guide for future resource use.

Other Data for Trend Definition

For the following data sets, we will enter the data to determine the approximate trend in order to make future predictions. We entered these numbers into the Statistical Graphical Tool in to determine some growth rates. There are four things to notice:

  1. In some cases the data is very will fit by a single exponential growth rate. In such a case, just a few years data is needed to make accurate predictions.

  2. In some cases, (i.e. software, canadian gas sales) there is a clear change in the rate of exponential growth. This can make trend extrapolation difficult and one has to consider if external factors caused a growth change and if those external factors are likely to continue. The regional air traffic data is a case in point where a different regulatory environment may have deterimental effects on the number of passengers.

  3. In a few cases, the rate of growth is continually increasing. This is the case for pollution costs as a percentage of GNP. Accurate trend extrapolation in this case is not possible.

  4. In still other cases, while there is a single growth rate that reasonable fits the data, there are significant oscillations about that growth rate. These represent intrinsically noisy systems which make short term trend predictions difficult, but long term trends remain well defined by the single growth rate.

Okay Here is a bunch of Data to analyze. If you weren't in class it would be useful to enter some of the data into the exponential growth tool referenced above.

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