Final answer:
To determine the increase in generating capacity needed after a decade with a 9% annual increase, we use the compound growth formula. The capacity must be increased by approximately 235.26%, indicating how much additional capacity is needed to meet the forecasted demand.
Step-by-step explanation:
The student's question revolves around calculating the increase in a utility company's generating capacity to meet future electricity needs based on a 9% annual increase in consumption. To find the compounded increase in generating capacity after a decade, we can use the formula for compound growth, which is A = P(1 + r)^n, where A is the amount of increase, P is the initial capacity, r is the rate of increase (expressed as a decimal), and n is the number of periods or years.
Step-by-Step Explanation:
Express the 9% increase as a decimal, which is 0.09.
Apply the formula for compound interest to predict the future capacity after 10 years, considering that n equals 10.
Calculate the resulting amount which tells us the factor by which the initial capacity must be multiplied to achieve the required capacity at the end of the decade.
Subtract 1 from this factor and multiply by 100 to convert it to a percentage, which will reveal the percentage increase in capacity needed.
Since we do not have the initial capacity (P), we are only calculating the factor, not the actual capacity in watts or other units. Instead, the final result will give us the percentage increase in capacity needed.
By applying these steps, we can find that the utility company will need to increase its generating capacity by (1 + 0.09)^10 - 1, which is approximately 1.9 or 235.26% when converted to a percentage and rounded to two decimal places.