Energy and Human Ambitions on a Finite Planet, 2021a

1 Exponential Growth 7
We can check the result using Eq. 1.6 by putting in t 22.5 <strong>and</strong>
p 0.05 or t 2 14.2 in the latter form.
1.2 Exponential <strong>Energy</strong> Extrapolation
Having established some basic principles of exponential growth, it’s time
for a first look at how we can use the math to argue about limits to our
expectations. We’ll concentrate on energy use. The United States <strong>Energy</strong>
Information Administration (EIA) provides information on energy use
from 1949 to the present. An appendix (E1: [3]) presents an approximate
account of energy use from 1635–1945. Figure 1.2 displays the more
recent portion of this history.
Lacking comparable data for the world, we
use U.S. data simply to illustrate the more
broadly applicable global growth trend.
Even countries far behind are growing energy
use—often faster than the 3% characteristic
of U.S. history.
1e12
4.0
3.5
<strong>Energy</strong> Production Rate (TW)
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1800 1850 1900 1950 2000
year
Note that the energy rate at the left edge of Figure 1.2 becomes almost
invisibly small. Presenting the data on a logarithmic plot, as in Figure
1.3, we can better see the entire trajectory. On such a plot, exponentials
become straight lines. The trend is remarkably consistent with an exponential
(red line) for most of the history, at a rate just shy of 3% per year.
Note that this total effect includes population growth, but population
has not grown as fast as energy, so that per-capita energy has also risen.
This makes sense: our lives today are vastly more energetically rich than
lives of yesteryear, on a per-person basis.
Having established that energy growth over the past several centuries
is well-described by an exponential, we can explore the implications of
continuing this trend forward. Starting at a present-day global energy
production rate of 18×10 12 Watts (18 TW), we adopt a convenient growth
rate of 2.3% per year for this exercise. We pick this for two reasons: 1) it
is more modest than the historical trend, so will not over-exaggerate the
Figure 1.2: U.S. energy over 200 years, showing
a dramatic rise due almost entirely to
fossil fuels. The red curve is an exponential
fit tuned to cover the broader period shown
in Figure 1.3.
The astute reader might note a departure
from the exponential fit in recent years. This
only reinforces the primary point of this
chapter that sustaining exponential growth
indefinitely is absurd <strong>and</strong> will not happen.
If growth is destined to stop, perhaps we
are beginning to experience its limits well
before the theoretical timescales developed
in this chapter.
Watts is a unit of power, which is a rate of
energy. Chapter 5 will cover the concept
<strong>and</strong> units more thoroughly.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.