Math 114Q, Section 10
First Exam
October 4, 2007

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 over the weekend. Write "I understand the instructions" in your blue book for a free 5 points.

  2. (5 points) The United States was created in 1776. How old is it in seconds? Write your answer in metric terms with the proper prefix - kiloseconds or petaseconds or whatever is appropriate.

  3. (20 points) The item you've found marked $64.99 in Filene's Basement has been on the rack for so long that the Automatic Markdown System tells you it's 50% off. The sticker says "take another 15% off!"

    1. Calculate your savings in dollars and as a percentage of the original marked price.

    2. Filene's bought that item from their supplier for $25.00. What is their profit as a percentage of their cost?

    3. What would their profit as a percentage of their cost be if they'd sold the item at the original price?

    4. (Extra Credit) What is Filene's Basement's Automatic Markdown System?

  4. (25 points) The UMass Boston annual operating budget this year is about $237 million (www.umb.edu/administration_finance/budget_office/budget_07.html).
    Student fees are about $3600/year for Massachusetts residents (umb.edu/administration_finance/bursar/tuition_fees.html#u_instate).
    There are about 13,300 students (www.umb.edu/about/)

    1. What percentage of the operating budget is covered by student fees?

    2. If the annual inflation rate is 4.5%, what will next year's operating budget need to be to offer the same services?

    3. The easiest way for the Chancellor to raise all the extra money is to raise student fees. He knows that would be unpopular (and unfair), so wants to know how much those fees would have to increase before he makes his decision.

      If the total increase in expenditures is to be funded entirely by raising student fees, how much will each student's fees need to go up (give both an absolute answer in dollars and a percentage increase).

    4. The answer you've found in (c) depends on several approximations and assumptions. It ignores the fact that some students have fee waivers, some are part time only, that fees for out of state students and graduate students are larger, and that the number of students may be different next year. How reliable is your answer, given these uncertainties? Could you trust it as a basis for deciding whether to cover the budget shortfall just by raising fees, or would you need a more accurate estimate?

  5. (25 points) The Business/Money section of The Boston Globe, Sunday 9/30, carried an article on Power Shifting: charging more for electricity during the day than at night. The article reported on one family's experience with this experiment:
    During the past year, the [Winslows] used just over 20,000 kilowatt-hours of electricity, of which 85% was consumed during off peak hours. Their power shifting saved them $348. ...

    Instead of paying the standard delivery charge of 6.2 cents per kilowatt hour all day long, the Winslows pay $13.95 cents from 9 a.m. to 6 p.m. weekdays and 3.4 cents from 6:01 p.m. to 8:59 a.m. on weekdays and all day weekends. Because they require a special meter, their fixed monthly customer charge is $9.99 instead of the standard $6.43.

    1. What would the Winslow's electric bill for the year have been if they had not been participating in the experiment?

    2. What was their electric bill?

    3. Do your calculations confirm what the article says about the Winslows' savings?

  6. (20 points) On July 22, 2007 The New York Times reported that
    In its first 24 hours on sale, Harry Potter and the Deathly Hallows, the seventh and final installment in the wildly popular series by J.K. Rowling that officially went on sale at 12:01 a.m. Saturday, sold a record 8.3 million copies in the United States, according to Scholastic Inc., the book's publisher.

    1. On the average, how many books per minute were sold during that first day?

    2. Estimate how many bookstores were selling the book. (There's no single correct numerical answer to this question. Be sure you clearly state the assumptions you make that lead to your estimate.)

    3. (Extra Credit). In Harry Potter's wizard world currency is measured in Galleons, Sickles and Knuts. 1 Galleon = 17 Sickles; 1 Sickle = 29 Knuts.

      Scholastic Books, the publisher of the Harry Potter series in the United States, has issued paperback copies of books that (they claim) Harry Potter used at Hogwarts. The image shows the price of one of these books in dollars and wizard money. Use this information to figure out the number of Dollars per Galleon.

      The list price of Harry Potter and the Deathly Hallows is $34.99. How many Galleons is that? (You may write your answer with decimal fractions of a Galleon. No need to convert the fractional part to Sickles and Knuts - but you can if you want to.)

  7. Extra Credit - start this question if you have time. If you don't, work it out at home over the weekend.

    1. How much energy does burning our imported oil generate in a year? Express your answer in metric terms with the proper prefix - gigawatt-hours, or terawatt-hours, or petawatt-hours, or whatever is appropriate.

    2. The oil we import isn't used primarily to generate electricity. But if it were, how many families like the Winslows (see question 4) would it provide electricity for?

    3. Estimate how many oil tankers it would take to deliver the 10 million barrels of oil we import each day.