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energy consumption over the past 200 years. It is plainly obvious that energy use has been growing nonlinearly; the line on the chart looks like one of our hockey sticks. Can energy consumption grow exponentially forever, or is there some sort of a limit, a defined capacity to the energy stadium, that would cause us to fix the left axis on this chart?
Figure 5.6 Total Energy Consumption
This chart includes energy from all sources: hydrocarbons, nuclear, biomass, and hydroelectric.
Source: Vaclav Smil, Energy Transitions.
On the following page is another exponential chart—the U.S. money supply, which has been compounding at incredible rates ranging between 5 and 18 percent per year ( Figure 5.7 ).
Figure 5.7 Total Money Stock (M3)
This was the widest measure of money before its reporting was discontinued by the Federal Reserve. M3 money included cash, checking and savings accounts, time deposits, and Eurodollars.
Source: Federal Reserve.
These are just a few examples. We could review hundreds of separate charts of things as diverse as the length of paved roads in the world, species loss, water use, retail outlets, miles traveled, or widgets sold, and we’d see the same sorts of charts with lines that curve sharply up from left to right.
The point here is that you are literally surrounded by examples of exponential growth found in the realms of the economy, energy, and the environment. Far from being a rare exception, they are the norm, and because they dominate your experience and will shape the future, you need to pay attention to them.
The Rule of 70
As I said before, anything that is growing by some percentage is growing exponentially. Another handy way to think about this is to be able to quickly calculate how long it will take for something to double in size. For example, if you are earning 5 percent on an investment, the question would be, How long will it be before a $1,000 investment has doubled in size to $2,000? The answer is surprisingly easy to determine using something called the “Rule of 70.” 1
To calculate how long it will be before something doubles, all we need to do is divide the percentage rate of growth into the number 70. So if our investment were growing at 5 percent per year , then it would double in 14 years (70 divided by 5 equals 14). Similarly if something is growing by 5 percent per month , then it will double in 14 months.
How long before something growing at 10 percent per year will double? Easy; 70 divided by 10 is 7, so the answer is 7 years.
Here’s a trick question: Suppose something has been growing at 10 percent per year for 28 years. How much has it grown? Some people intuitively guess eight times larger (2 + 2 + 2 + 2 = 8), or four separate doublings over each of the four 7 year periods in the example, but the answer is sixteen, because each doubling builds off of the last (2 ⇒ 4 ⇒ 8 ⇒ 16). Two doubles to four, which doubles to eight, which doubles to sixteen, which is twice as large as intuition might suggest.
Here’s where we might use that knowledge in real life. You might have read about the fact that China’s energy consumption grew at a rate of slightly more than 8 percent between 2000 and 2009, which perhaps sounds somewhat tame. Using the Rule of 70, however, we discover that China is doubling the amount of energy it uses roughly every 9 years, as was confirmed by the International Energy Agency (IEA) in 2010. 7 After 9 years of 8 percent growth, you’re not using just a little bit more energy, but 100 percent more. If a country has 500 coal-fired electricity plants today, after 9 years of 8 percent growth it will need 1000 such plants.
If this seems rather dramatic and nontrivial to you, you’re right. Time for another trick question about doublings: Which is larger in size, the amount of energy China used over just the past 9 years (its most recent doubling time), or the
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