2.4: Growth in Energy Demand

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Page ID: 47160

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Growth in the world and the U. S. energy consumption as a function of time, follow what is known as exponential function. The exponential increase is characterized using

\[ \dfrac{ \Delta N }{ \Delta t } \varpropto \, N \]

\[ \dfrac { \Delta N }{ \Delta t } = \lambda N \]

where Δ (the Greek letter delta) is the change or increment of the variable and λ (lambda) is the growth rate. After some mathematical methods, it can be shown that the equation changes to the form

\[ N = N_0e^{λt} \]

where \( e \) is a constant that equals 2.71.

We can determine how long it takes for \( N_0 \) to become \( 2N_0 \) (twice its original number or double). That time period is called doubling time. After some mathematical steps it can be written as

\[ Doubling \, Time = \dfrac{ 70 } { \% \, Growth \, Rate \, per \, Year } \]

Example

Use of coal is projected to increase at the rate of 1.7% per year in the U.S. How long will it take to double its usage?

Answer

Using equation 2.4.4,

\[ Doubling \, Time \, (years) = \dfrac{70}{1.7} = 41.17 years \nonumber\]

Thus, in 41.17 years, the consumption of coal will be twice as much as it is today.