A utility company in a western city of the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population. If consumption does increase at this rate, find the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade.

Question

Nylah Benjamin

Mathematics

10 April, 13:08

A utility company in a western city of the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population. If consumption does increase at this rate, find the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade.

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Mike Jimenez · Answer 1

Let C₀ be current consumption. Then consumption (C) after t years is:

C (t) = C₀ * (1 + 0.1) ^t

C (t) = C₀ * (1.1) ^t

After 10 years, consumption will be:

C (10) = C₀ * (1.1) ^10

C (10) = 2.5937424601 C₀

Total percentage increase after 10 years:

(2.5937424601 C₀ - C₀) / C₀ = 1.5937424601 C₀ / C₀ = 1.5937424601 = 159.37%

Utility company will have to increase generating capacity by 159.37%