Mathematical and Technological Literacy I Activity 2:  Exponential Modeling

Please do the following at the beginning of every computer activity.

a. Open a new Word document.

b. Click on the Office Button in the upper left corner, then slide over "Save As".   Choose either "Word Document" to save your document as a Word 2007 document or "Word 97-2003 document" to save your document in an early version of Word.  If you are not sure which to choose, you should use "Word 97-2003 document".  Save the document to the desktop by setting the "Save in" textbox to "Desktop". (Saving to the desktop makes it easy to retrieve your work when you are finished.)  Your file name should be entitled something like "Group Activity 2".  Last, confirm the save as type in the last box.  (*.docx) is the suffix for a Word 2007 document.  (*.doc) is the suffix for early versions of Word.

Learning Goals for this Activity

1. You will continue to develop your Excel skills of creating tables.
2. You will understand some of the characteristics of exponential growth, especially its eventual rapid growth.
3. Given a reference value and the relative increase or decrease, you will be able to calculate the resulting amount.

1. Suppose a magic genie gives you a choice. He will give you $1000 each day in the month of March or he will give you 1¢ on the March 1st, 2¢ on March 2nd, 4¢ on March 3rd, doubling the amount each day.

a. Without thinking about it too hard, which would you pick?

b. Open the file genie.xls.  Extend the table for all 31 days. Paste it into your Word document.

Day	Amount given on each day under option 1	Total for option 1 on each day	Amount given on each day under option 2	Total for option 2 on each day
1	$1000	$1000	$0.01	$0.01
2	$1000	$2000	$0.02	$0.03
3	$1000	$3000	$0.04	$0.07

c. What does the table show? Would you change your mind about the which deal to pick?

d. At what point in your table is the amount in the fifth column in your table larger that the amount in the third column?

e. Plot the two total columns under each option on the same chart as separate series (To do so you need to select the data in columns A,C, and E; use an xy scatter plot).   You won't be able to graph for option 1.  In order to see it better, you may want to adjust the scale of the y-axis.  Right click on the y-axis and select Format Axis.  Under Axis Options you can set the minimum and maximum by first selecting Fixed, and then entering the new value in the box on the right.  A maximum of about 100,000 gives a nice view.   In a brief paragraph describe the salient features of the graph.

2. Determine if each of the following tables represents a relationship that is linear or exponential. For your convenience, these tables can be found the in Excel file Linear_Exponential.xls. Each table is on a separate sheet within this file; click on the worksheet tabs on the bottom of the window to display each one in turn.

a.

b.

c.

3.  Using the formula above, solve the following problems:

a.  Percentage Increase:  The Lexus, LX470 costs 35% more than the Mercedes, ML500.  If the price of the Mercedes, ML500 is $56,750, what is the price of the Lexus, LX470?

b.  Percentage Decrease:  A department store advertises jeans for 30% off the original price.  If the original price of the jeans is $60, what is the sales price?

c.  Percentage Increase:    On August 12, 2005, one share of Lucent stock cost $2.95.  On September 8, 2005, the stock closed 7.8% higher.  What was the cost of one share of Lucent stock on September 8th?

d.  Percentage Decrease:  Sue went on a weight loss program an lost 10% of her weight.  If Sue weighed 150 pounds prior to her weight loss, what did she weigh after her weight loss?

e.  Percentage Increase:    If the population of the state of Illinois is 104% larger than the population of Indiana in 2000, what was the population of Illinois if the population of Indiana was approximately 6,080,000?

4. The population of the Russia in 1998 was 147 million; the population of Nigeria was 106 million.  Russia is decreasing in population by approximately 0.1% annually; the population of Nigeria is growing at 3%.  Using Excel, predict the year when Nigeria's population will exceed Russia's, assuming that the current trend continues.  How much faith do you have in your answer? What factors could affect the validity of your prediction?

5.  World oil production was 518 million tons in 1950.  Between 1950 and 1972, production increased at a rate of 7% per year.  World oil production in 1998 was approximately 3300 million tons.

a.  Using the information above, estimate the world oil production in 1972?

b.  Using the result of part a, determine how much oil would have been produced in 1998 if growth in production had continued at a rate of 7% between 1972 and 1998.  Compare this result to the actual 1998 figure given above.

c.  Using the result of part a, determine how much oil would have been produced in 1998 if growth in production had proceeded at a rate of 3% between 1972 and 1998.  Compare this result to the actual 1998 figure given above.

d.  Using your answer from part a, estimate the actual annual growth rate in world oil production between 1972 and 1998.