Mathematics, 20.07.2019 21:40 speedyblackmann

Based on the yearly average values, calculate one person's residential electricity needs for a year.

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Part A:

From the given graph, the average monthly per capita residential use of electricity in the United States in 2004 is 370 Kilowatt-hours.

Therefore, the average yearly per capita residential need for electricity is given by:

370 x 12 = 4,440 Kilowatt-hours.

Part B:

From the given graph, average influx of solar radiation per square meter for Topeka, Kansas is 130 Kilowatt-hours.

Therefore, the average yearly solar radiation per square meter is given by:

130 x 12 = 1,560 Kilowatt-hours.

Part C:

Assuming that photovoltaic conversion of solar energy has 10% efficiency.

The number square meters of photovoltaic cells that would be needed to supply one person's electricity for the year, based on the yearly average values is calculated thus:

Recall that from part A we have that the average yearly need of electricity per person is 4,440 kilowatt-hours and from part B, we have that the average radiation per square meter for the year is 1,560 kilowatt-hours.

Thus, the number of square meters that will produce 4,440 kilowatt-hours of electricity is given by:

$\frac{4,440}{1,560} =2.85m^2$

Given that the photovoltaic conversion of solar energy has 10% efficiency, therefore, the number of square meters of photovoltaic cells that will produce 4,440 kilowatt-hours of electricity is given by:

$\frac{2.85}{0.1} =28.5m^2$

Part D:

From part C, we have that the number of square meters that will produce 4,440 kilowatt-hours of electricity is 2.85m^2

If the efficiency of photovoltaic cells is 40%, the number of square meters of photovoltaic cells that will produce 4,440 kilowatt-hours of electricity is given by:

$\frac{2.85}{0.4} =7.12m^2$

Part E:

Given that commercially available household photovoltaic systems cost approximately $20,000 and that the average cost of electricity in the United States is approximately $0.09 per kilowatt hour.

If the the system is installed for a four-person household, the amount of electricity needed per year by a four-person household is 4,440 x 4 = 17,760 kilowatts-hour and the cost of electricity for the four-person household is 17,760 x 0.09 = 1,598.4

Therefore, the number of years it will take the photovoltaic system to generate $20,000 of electricity is given by:

$\frac{20,000}{1,598.4} \approx12.5\ years$

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What is the domain and range of this graph?

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