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.  Magic Genie: 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 by adding the following formulas into the specified cells of row 3:

Col A: A2+1

Col B: =B2

Col C: =C2+B3   [This adds each days gift to the previous total.]

Col D: =D2*2

Col E: = E2+D3

Select rows 5-28 and hide them.  [Click: Format --> Row --> Hide).  Paste the remaining rows into your Word document.  Unhide the hidden rows. 

c. What does the full 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. Make separate XY scattergrams and copy them into your Word document.  In a brief paragraph, compare their shape. 

2.     Population growth:  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 the simulation method, 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?

3.      Oil production.  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.  Based on the information above, and using the exponential growth formula, predict precisely the amount of 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.