Throughout the 20th century, the yearly consumption of electricity in the US increased exponentially at a continuous rate of 7% per year. Assume this trend continues and that the electrical energy consumed in 1900 was 1.4 million megawatt-hours.
Find the average yearly electrical consumption throughout the 20th century.
after n years,
energy = e(n) = 1.4*10^6 * 1.07^n
e(100) = 1213.8*10^6
(1213.8 - 1.4)*10^6/100 = 1212.4*10^4 = 12.124 megawatt-hr/year
To find the average yearly electrical consumption throughout the 20th century, we need to calculate the average of the consumption in 1900 and the projected consumption in the year 2000.
First, let's calculate the projected consumption in the year 2000 using the exponential growth rate of 7% per year.
We can use the formula for exponential growth: A = P * (1+r)^t, where:
A is the final amount (projected consumption in the year 2000),
P is the initial amount (consumption in 1900),
r is the growth rate (7% or 0.07), and
t is the number of time periods (in this case, 100 years).
So, we have A = 1.4 million * (1 + 0.07)^100.
Calculating this, we find that the projected consumption in the year 2000 would be approximately 156.57 million megawatt-hours.
Now, to find the average, we add the consumption in 1900 to the projected consumption in 2000 and divide by 2:
Average = (1.4 million + 156.57 million) / 2
Calculating this, we find that the average yearly electrical consumption throughout the 20th century is approximately 78.99 million megawatt-hours.