Trend Extrapolation

# 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

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.

• Number of Scanners Sold since 1991: 1.8 2.3 2.5 2.9 3.3 3.5 3.9

• Number of Network Connectors Sold since 1991: 44 59 77 88 103 122 148

• Software Sales: 2.5 3 3.4 4.3 5.5 6.5 7 8 10 12.5 18 21 23.5 28.2 35.3 40.7 45.0 53.9 68.1 79.9 94.1 107.2 122 138.9 157.2 178

• Mens Underwear Production Payroll: 85 91 97 116 107 130

• Womens Outerwear Production Payroll: 109 110 115 110 108 126 122

• Value of the Metal Furniture Industry: 159 170 180 183 190 214 222

• Pharmaceutical Industry: 189 212 228 282 329 358

• Canadian Natural Gas Sales: 313 314 328 339 339 345 433 402 428 450 435 404 451 489 475 481 501 541

• US energy consumption since 1991: 81.1 82.2 83.9 85.9 87.2

• World Fiberboard Importation Value: 401 422 372 391 501 628 732 768 998 1007 1259 1320

• Cable TV Revenues: 98 167 195 268 379 496 635 787 957 1223

• Public Share of National Debt: 205 219 241 269 308 343 365 384 403 421

• Coal Generating Capacity since 1990: 2547 2306 1861 2028 3233 4859

• 9-12 grade enrollments in Oregon: 143 137 141 144 149 154 156

• 9-12 grade enrollments in California: 1352 1373 1410 1449 1503 1559 1615

• Higher Ed National Enrollments: 108 107 109 108 110 110 112 113 115 116

• Pollution Costs as % of GNP: 1.5 1.7 1.8 2.0 2.3 2.4 2.8 3.4 3.8 4.4 5.2

• Amount of Solid Waste Increase since 1960 (every 5 years): 143 145 142 140 153 152 157 161 164

• Number of Automobiles Miles since 1975 (every 5 years): 8.5 9.6 9.0 9.4 9.7

• Regional Aircarrier Passagner Traffic since 1980: 14 15 17 20 22 23 25 27 30 32 35 37.5 40 42 45 49 52