Possible extra exam questions. ---------------------------------------------------------------------- Note: I think Mark is wrong to want two separate charts for the linear and exponential trendlines. Yes, it's a little easier for them to draw. But much of the point of the exercise is lost if they can't visually compare the lines. ---------------------------------------------------------------------- Why might a high definition TV costs $600 this Christmas season. Suppose the inflation rate is 5% per year. a) How much will the television set cost three years from now? b) How long until the price doubles? c) Why might the TV set not cost $1200 then, in spite of the inflation? --------------------------------------------------------------------- Reread question ? (blood circulation). Answer these additional questions. The heart pumps in order to circulate red blood cells around the body. x) How many times a day (on average) does a red blood cell complete a round trip from the heart out into the body and back? y) How long (on average) does each such trip take? ---------------------------------------------------------------------- Reread question ? (college tuitions). Answer these additional questions. x) Use Excel to draw a single chart displaying histograms for in state tuitions for the years 2006-2007 and 2007-2008. Use intervals of length $5000. [If you think this is too hard, make it for one of the years. They can do the double histogram for extra credit.] y) What is the probability that if you choose a college at random the 2006-2007 in state tuition there was more than [insert median value here]? z) What is the probability that if you choose a college at random the 2006-2007 in state tuition there was less than $15000? w) What extra information would you need to answer this question: what is the probability that if you chose an in-state Massachusetts college student at random his last year his or her tuition would have been less than $15000? ---------------------------------------------------------------------- Suppose you are considering buying a house that cost $zzz. You can afford a down payment of $www and must borrow the rest at an annual interest rate of 7.35%. a) How long will it take you to pay off the mortgage if you can afford to pay $yyy per year? How much interest will you pay? [Pick the numbers so that it's about 35 years - that will require them to extend the table in the paying down a debt spreadsheet] b) You usually write a check to the bank for your mortgage once a month, not once a year. How much interest would you pay on this mortgage if you did that? How much do you save compared to annual payments? Why is the total interest less? [This is essentially one we asked them on a hw many of them did not do. We could make it extra credit.] ---------------------------------------------------------------------- At the web site http://www.sec.state.ma.us/trs/trsbok/mod.htm you will find this paragraph: The Massachusetts State House cornerstone was laid on the Fourth of July, 1795, by Governor Sam Adams and Paul Revere, Grand Master of the Masons. The stone was drawn by fifteen white horses, one for each of the states of the Union at that time. The cost of the original building? $133,333.33 a) What is wrong with the last number? b) What would that number be in today's dollars? [I found two calculators on the web that would go back to 1800. They gave these answers $1,524,277.14 http://www.westegg.com/inflation/ $4,160,388.21 http://www.halfhill.com/inflation.html I think that even the second of these is too small. We could point them to both, or somehow ask the question so that it led them to distrust what they found on the web ... a useful thing. ] ---------------------------------------------------------------------- Do something with this, if not on the exam then in the book: New York Times Editorial The Prince and the Plane Published: November 14, 2007 On Monday, a Saudi billionaire, Prince Walid bin Talal, placed an order with Airbus for his new private plane, the A380. That superjumbo will be the largest private jet on the planet. No hard figures were mentioned, but the asking price for an A380, which weighs 200 tons more than a Boeing 747 and has a floor space of about 6,000 square feet, is around $300 million. That is for the raw plane itself, hull, wings, engines, etc. . nothing to distinguish its interior from the hold of a cargo plane. But even unfurnished, the purchase of this Airbus offers some interesting numbers to think about. For instance, the average-size house in America . about 2,300 square feet . would cost $106,812,000 at the price per square foot that Prince Walid paid. Even in California, this is a lot. Or think of it a different way. According to recent figures, a Manhattan apartment costs, on average, $1,013 a square foot. (Somehow that.s depressing enough in its own right.) At that rate, the prince.s $300 million would buy an apartment just under 300,000 square feet in size, a little more than six football fields. Throw in another $100 million or more to finish the interior of the plane to princely standards, and you.re talking real money. All this, and what you get is a plane parked on the tarmac. When Airbus describes the fuel consumption of the A380 . reportedly lower than that of a 747 . it says that it.s better .than a small car,. per passenger. But keep your eye on the .per passenger. number. Airbus assumes that the plane will be carrying 555 passengers. Prince Walid likes to travel with an entourage of 50. It.s safe to say that fuel consumption per passenger on these princely voyages will be astronomical . and, in terms of the prince.s pocketbook, inconsequential. Somehow, what we.re left with is the image of a plane that is meant to take off . into its own ever-warming atmosphere of unreality.