Activity 2 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. The Question:

If you worked four summers, starting at age 17, and invested the $2000 you earned each summer into an account that earns 10.7%, how much will you have in the bank at retirement age (age 67)?

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

          a.  $      25,917
          b.  $      71,625
          c.  $    197,943
          d.  $    547,037
          e.  $ 1,114,423

• Continue your age column year-by-year through age 67. 
• After making deposits for four summers, you will deposit no more money into this account.  In the cell B6, enter a formula to calculate the account balance at age 21 (use the exponential formula we learned in class).  Remember that the rate is 10.7%.  Fill down the formula in cell B6.  Type the balance at age 67 in your Word document.

c.  Are you a millionaire at age 67?  How does your balance at age 67 compare to your guess in "a"?

d.  Attached is the article Start your first $1 million at age 16.  If you compare the starting age in your Excel table to the starting age in the article you will notice that they are different.  How does this discrepancy affect the results in the article?  (Are the account balances in the article for ages 20, 30, 40, 50, 60 & 67 too high or too low?)

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 24% more than the Mercedes, ML500.  If the price of the Mercedes, ML500 is $54,530, 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.