Math 114Q, Sections 9, 11
First Exam
September 30, 2008
Answers

General guidelines Here are the questions:
  1. (5 points) Read the general guidelines - particularly the first two about the form your answers should take, and the chance to improve your answers between now and Thursday. Write "I understand the instructions" in your blue book for a free 5 points.
  2. (15 points) In a QR course that prides itself on paying attention to current events the first real question on this exam should start with the front page of today's Globe, where the lead story states that
    The Dow Jones industrial average suffered its worst one-day point decline in history ... The Dow closed on Friday at 11,143.13 points and closed on Monday at 10,365.45 points.
    You do not need to know what the Dow Jones industrial average is to answer this question (in fact we'll talk about the stock market later this semester).
    1. Calculate the change in the Dow between Friday and Monday in absolute and percentage terms.
    2. The article goes on to state that "...the percent decline does not rank in the top 10 of losses for the Dow." Does this contradict the opening sentence of the article? Explain how both statements could be true.
  3. (15 points) A 12 ounce package of Greenies costs $13.74. A 30 ounce package costs $26.99.
    1. Which size should I buy? Explain your answer.
    2. I have a coupon worth $5 toward the price of any package of Greenies. If I use the coupon, which size should I buy? Again, make sure you explain your answer.
    3. Is it always better to buy the large ecomomy size?
    4. Extra credit. What's a Greenie? Are these prices reasonable?
  4. (40 points) Refining the oil in a 42 gallon barrel produces about 19 gallons of gasoline; the rest is turned into products like jet fuel and heating oil. Right now oil sells for about $105/barrel.
    1. What percentage of the oil in a barrel is refined into gasoline?
    2. What is the dollar value of the gasoline in a barrel of oil?
    3. Find the value of that gasoline in dollars per gallon.
    4. The dollar value of the gasoline when it's refined from the oil in a barrel is only part of the cost at the pump when you fill your tank. Estimate the percentage of the cost that represents. What might account for the rest of the cost?
    5. In 1981 oil prices peaked at just over $78/barrel. Use the inflation calculator at the Bureau of Labor Statistics ( www.bls.gov/data/inflation_calculator.htm) to compare that price expressed in current dollars with the price now.
    6. Is gas more expensive now than it was in 1981? Make a comparison of gas prices between 1981 and 2008 using relative (or percentage) change.
    7. Use the web to verify three of the numbers we've used in this question: 42, 105, 20 million. For each, give the URL of the site where you find the information, and discuss any discrepancies.
    8. Extra credit. Answer the previous question for the numbers 19 and 78.
    9. Extra credit. The United States uses about 20 million barrels of oil each day. Estimate the value of that oil in dollars per person per year.
  5. (15 points) In an August 2008 post at www.ecogeek.org/content/view/2012/ Hank Green writes that "U.S. Wind Power Could Hit 150 Gigawatts by 2020".

    You do not need to spend time on this exam reading that article! You don't even need to know what a watt is.

    1. Later in the post the author says that "the average coal plant produces about 800 megawatts of power. So this is enough to displace about 180 coal plants." Check his arithmetic.
    2. Current United States power production is 3.3 Terawatts. The need will probably grow by 10% between now and 2020. What percentage of our needs will be met by wind power then if the prediction in the posting is correct?
  6. (10 points) The September 28, 2008 edition of The Boston Globe Magazine was devoted to the environmental issues. The article "In Praise of Plastic" began with this paragraph:
    "IN A WAREHOUSE IN CHARLESTOWN, plastic piles up by the truckload. Milk jugs sit atop soda bottles. Water bottles mingle with Tupperware lids. Not yet recycled but no longer useful, the plastic builds, undulating with peaks and valleys like a mountain range. There are even miniature avalanches as the plastic - maybe 100 tons of it - settles. And even though it is here to be recycled, given a second life as fleece jackets or plastic decking, for some, all this plastic looks like everything that's wrong with 21st century living."

    (You don't need to read the article, but if you're curious you will find it at www.boston.com/bostonglobe/magazine/articles/2008/09/28/i n_praise_of_plastic.)

    1. Estimate how long it takes the residents of Boston to generate 100 tons of recyclable plastic. (Remember that an estimate is not just a guess. It's a computation based on reasonable assumptions.
    2. Using your answer to part a), discuss whether the article's figure of "100 tons" is reasonable.