Group Activity 9 The Power of Exponential Growth

All group activities must include a statement signed by all members of your group that each group member fully participated in the activity. To start you should open a new Word document entitled something like "Group Activity 2" and put the names of your group members at the top. Save it to the desktop and save frequently during the hour.

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.  One of the options is Scale.  You can set the minimum and the maximum there.  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. 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?

4.  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.