Question

Find the number of years before the electric utilities will need to double their generating capacity.

a) This involves exponential growth calculations.
b) Electric utilities typically plan for long-term capacity doubling.
c) Mathematical modeling is used to predict doubling times.
d) Calculating doubling time involves growth rate analysis.

Answer 1

To find the number of years before the electric utilities will need to double their generating capacity, use the concept of exponential growth and the doubling time formula. Option A is correct.

Step-by-step explanation:

To find the number of years before the electric utilities will need to double their generating capacity, we can use the concept of exponential growth and the doubling time formula. The doubling time formula is given by the equation:

Doubling time = (ln 2) / (ln (1 + growth rate))

where the growth rate is a decimal value. Since the problem mentions a growth rate of 2.3%, we can convert it to a decimal by dividing it by 100, giving us a growth rate of 0.023.

Substituting the given values into the formula, we have:

Doubling time = (ln 2) / (ln (1 + 0.023))

Doubling time ≈ 30.65 years

Therefore, it will take approximately 30.65 years for the electric utilities to double their generating capacity.