8.4.2: Exercise 2.3-W Renewable Energy

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MAKING CONNECTIONS TO THE COLLABORATION

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

(i) Absolute change is measured as a quantity (for example, an increase of $3). Relative change is measured as a percentage compared to the reference value (for example, an increase of 3%).

(ii) To find relative change, subtract the original number from the new number and divide by the original.

(iii) Consider this situation: Quantity 1 increases by 15%. Quantity 2 increases by 20%. Quantity 2 must have increased by a larger amount than Quantity 1.

(iv) The need for more renewable energy requires that all countries use more solar power.

DEVELOPING SKILLS AND UNDERSTANDING

(2) The following headlines all refer to change. Identify the change as absolute or relative.

(a) “Enrollments at Northeastern University are expected to increase by 1,500!”

(i) Absolute change

(ii) Relative change

(b) “Another 14% tuition increase is expected.”

(i) Absolute change

(ii) Relative change

(i) Absolute change

(ii) Relative change

(d) “A new proposal has sales tax rates dropping from 3% to 1%, a 67% drop!”

(i) Absolute change

(ii) Relative change

(3) The two questions below refer to data taken from the U.S. Census.³ The dollar values take into account the changes in the economy over the years (i.e., inflation).

(a) A typical high-income household in 1980 earned $125,556. A similar household in 2009 earned $180,001. What was the relative increase in income for these households from 1980 to 2009? Round to the nearest one percent.

(b) A typical middle-income household in 1980 earned $34,757. A similar household in 2009 earned $38,550. What was the relative increase in income for these households from 1980 to 2009? Round to the nearest one percent.

(4) After the U.S. Congress passed temporary tax cuts in 2010, persons in the U.S. who earned $50,000 per year had a lower tax rate. On average, these persons retained 2% more of their income than before the cuts. The 2010 law also gave the same persons a separate $850 credit on their federal tax return.

(a) How much extra money did a typical person earning $50,000 receive due to the federal tax cuts?

(b) This extra money represents what percent of the typical person’s salary? Round to the nearest tenth of a percent.

(5) Due to the same 2010 law, persons earning $500,000 per year were taxed at a lower rate on the first $106,800 they earned, saving them 2% of this portion of their salary. The same persons also received $14,250 more on their federal tax return. Fill in the blanks to complete the statements below.

(a) A person earning $500,000 a year received $___________ more of their income. Round to the nearest dollar.

(b) A person earning $500,000 a year received ___________% more of their income. Round to the nearest tenth of a percent.

MAKING CONNECTIONS ACROSS THE COURSE

(6) In Collaboration 1.4, you used results from the 2012 Consumer Expenditure Survey on how Americans spend their income. A summary of this information is given in Table 1.⁴

Table 1: Percentages of Average Annual Household Expenditures

Housing	32.83%
Food	12.83%
Transportation	17.49%
Everything Else	36.85%

Which pie chart best represents the data given in Table 1?

(i)	(iii)
(ii)	(iv)

(7) Many egg producers keep chickens in small cages that do not allow the chickens to move. Some people believe that this is unhealthy, so they buy eggs from chickens that are not caged 24-hours a day. These are sometimes called “free-range” chickens. The United States Department of Agriculture (USDA) allows chickens to be called free-range as long as the chickens spend some of their time outside. The European Union (EU), however, has several additional restrictions. One of these is that the farmers must provide enough outside area so that if all the chickens were outside, the density of chickens would be no more than 0.25 chickens/sq meter.⁵

(a) How many square meters does the EU require for one chicken?

(b) A farmer in the United States wants to meet the EU guidelines. She measures her area in square yards (1 sq meter = 1.196 sq yards). How many square yards does she need for 1,100 chickens?

(i) 301.1 square yards

(ii) 4,400.0 square yards

(iii) 4,812.2 square yards

(iv) 5,262.4 square yards

______________________________________

³ https://www.census.gov/data/tables/time-series/demo/income-poverty/historical-income-households.html

⁴ http://www.bls.gov/cex/csxann12.pdf

⁵ http://en.Wikipedia.org/wiki/Free_range_eggs

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