8.8.2: Exercise 3.2-W Solar Energy

MAKING CONNECTIONS TO THE COLLABORATION

(1) Which of the following was one of the main mathematical ideas of the collaboration?

(i) Solar energy is the most efficient form of renewable energy.

(ii) A small difference in rounding does not make much difference in results.

(iii) A small difference in rounding can significantly change results when working with large numbers.

(iv) You can calculate the cost of gas per mile by dividing the price of gas by the gas mileage of
the car.

DEVELOPING SKILLS AND UNDERSTANDING

(2) In Arizona, there is bright direct sunshine throughout much of the year. A 5 Kw solar energy system can collect 9000 kWh of energy per year if installed on the south-facing roof of a building. However, in Arizona, electricity is eleven cents per kilowatt hour. The average Arizona home uses 66 million BTU per year.

(a) Given that 1 BTU = 0.000293 kWh, find the number of kilowatt hours used by the average home in Arizona in a given year.

(b) How much does a typical Arizonan homeowner spend on electricity per year?

(c) If a typical Arizona household were to install a 5 kW solar energy system, how much would it save on electricity per year?

(d) Given that the 5 kW system would cost $20,000 to install (minus a 30% federal tax credit), how many years would it take to recoup the initial investment?

MAKING CONNECTIONS ACROSS THE COURSE

(3) One way to compare the solar power capabilities between New Jersey and Arizona is by using the Sun Index. California has a Sun Index value of 1, Arizona’s index value is 1.18, and New Jersey’s index value is 0.81. How much sunlight does Arizona get compared to New Jersey? Write your answer as a percent.

(4) The National Center for Children in Poverty (NCCP) posted the following information in 2011:

Nearly 15 million children in the United States—21% of all children—live in families with incomes below the federal poverty level ($22,050 a year for a family of four).¹

(a) The graph below can be used to illustrate the statement from the NCCP. Identify what each section and the full circle represent in terms of the context and the percentage. Section 1 is the darker section.

The full circle represents _____________________________________and is _______%.

Section 1 represents ________________________________________and is _______%.

Section 2 represents ________________________________________and is _______%.

(b) Can the statement from the NCCP be restated to say that 21% of people below the federal poverty level in the United States are children? Select the best answer.

(i) Yes, because the reference value in both statements is the children in the United States.

(ii) Yes, because both statements are about children living in poverty so the percentages are the same. The reference values do not matter.

(iii) No, because the percentage of children is really much higher because families really need much more money than the federal poverty level.

(iv) No, because the reference value in the first statement is the total number of children. The reference value in the second statement is the total number of people below the poverty level.

(c) Based on the information in the paragraph, which of the following is the best estimate for the number of children in the United States in 2011?

(i) 30 million

(ii) 75 million

(iii) 100 million

(iv) There is not enough information to make an estimate.

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¹ http://www.nccp.org/topics/childpoverty.html