1. Compare electricity cost in England in 2005 (date of this sample bill) to cost in Boston today. (You'll need to convert British money in 2005 to dollars, then do something with inflation -- remember how to use the consumer price index calculator.)

2. Do the rest of the problems in the Tamworth document.

AT&T offers the following three calling plans for long distance land-line phones:

Calling Plan	        Description	             Monthly Fee  Long Distance rate
Unlimited Plus Plan	Unlimited calling to         $29.95        Included in monthly fee
                        anyone in the U.S., 24
                        hours a day, 7 days a week	

One Rate 7 Plus Plan	One low long distance rate,  $3.95         7 cents per minute
                        all day every day!

One rate 10 Plan	One low long distance rate,  None	  10 cents per minute 
                        all day every day
                        with no monthly fee	

Use Excel to draw one graph showing how the monthly bill (y axis) depends on the number of minutes you use the phone for long distance calls (x axis) for each plan.

Create a sequence of cells in column A for the various possible numbers of minutes. (Start with 0. What's a good step to use? What's a reasonable place to stop?) Don't type in all the entries by hand: use Excel to create the list.

Use columns B, C and D for each of the three plans. The fixed charge and charge per call should be in cells in those columns too, so you can use the same formula everywhere in the data table. (That will call for judicious use of the '$' to keep Excel from changing row numbers when you don't want it to.)

Since we want to see how you did the problem as well as the result, print the spreadsheet (with the graph on it) so that we can see the formulas, not the values. There's a trick for that. If you click anywhere in the spreadsheet outside the graph and then hold down the control key (it may be something else on the mac) while typing the backwards single quote (`) Excel will display the formulas, not the values (I learned this trick from Excel help). Do that, print the spreadsheet, and then control-` again to see the numbers.

Write a paragraph explaining to your friend how she should go about choosing the plan that's best for her. (Hint: finding the places where the lines in your Excel chart cross is the key to the problem. You can do that with Excel experiments or with algebra.)

Driving the fare hikes are oil prices approaching the symbolic milestone of $100 a barrel. Crude oil for December deliveries closed at $95.46 a barrel yesterday in trading on the New York Mercantile Exchange. A $1-a-barrel increase adds about $470 million a year to the cost of the US airline industry, according to the Air Transport Association, an industry trade group in Washington.

At a consumption rate of 19 to 20 billion gallons per year, every penny increase in the price of a gallon of jet fuel drives an additional $190-200 million in annual fuel costs for U.S. airlines. So if the price were a dollar higher over the course of one year, that would translate to about $19-20 billion more in operating expenses. According to the ATA quarterly airline cost index, fuel has overtaken labor as the industry's top cost and now constitutes 20 percent to 30 percent of industry operating expenses.

1. The Globe story states a rate of change for annual airline fuel cost as a function of oil price as

   
         470 million dollars
         -------------------
         1 dollar per barrel
   

   How much would annual fuel price increase if oil prices rose by $1.50 per barrel? If oil prices rose by $2.00 per barrel? If oil prices rose by $0.50 per barrel?

2. The ATA website also provides rate of change information for the fuel cost, but in different units. Write that rate of change clearly (as we did in part a) and then use it to calculate the increase in fuel costs if oil prices increased by 20 cents per gallon.

3. Verify the statement "...if the price were a dollar higher over the course of a year, that would translate to about $19 - 20 billion more in operating expenses."

4. Is the rate of change in the Globe story consistent with the rate of change on the ATA website? (Don't just answer "yes" or "no" - explain how you came to your opinion.)

5. The last part of the ATA statement claims that "fuel...now constitutes 20 percent to 30 percent of industry operating expenses." Use this and the other information in the paragraph to estimate total annual airline operating expenses.

Unfortunately, you need to get the numbers one at a time. We can't find an easy way to download them all at once.

Does the graph look linear? Fill an Excel column with a linear function that looks as close as you can make it to the real data. (Play with the slope and the intercept.) Plot the real data and the line on the same graph.