Group Activity 3a Exponential Growth and Percentage Change

In each case, in addition to giving the answer, write down the calculation you used (e.g. if the question were asking about the percentage increase for a quantity that increases from 8.3 to 9.2, write something like "(9.2 - 8.3)/8.3" along with the answer of 10.8%.)

In answering these questions, I suggest you try to think about them in terms of multiplicative growth factors.  I think you will find them easier that way.  So if something decreases by 15%, think of it as multiplying by 0.85.  If something increases by 3%, think of it as multiplying by 1.03.

1.  A item is on sale at a store with a 15% discount.  In addition you have a coupon that allows you to deduct an addition 25% off the purchase of one item.  If you use the coupon on this item, what is total percentage discount?  The answer is not 15% + 25% = 40%.

2. Intel Corporation stock rose 67% from January to March 2000.  In April it lost 24%.  By how many percent was the price of the stock higher than in January in April after the loss?

3. a. Suppose a stock decreases in value by 50% one year.  The next year it increases by 50%.  By how many percent has the value of the stock changed over the two year period?  Give your answer and briefly describe your reasoning.

b.  Suppose a stock decreases by 20%.  By how many percent must it increase in order to get back to even?

c.  Suppose a stock decreases by 60%.  By how many percent must it increase in order to get back to even?

4.  A population is growing at 3% annually.   By how many percent does it grow over 20 years?

5.  Consumer debt has soared 39% in total over the last five years and is now $1.3 trillion.   What was consumer debt five years ago?

6.  The population of Nigeria has been growing at 2.8% per year.  If its population in 2003 was 140.6 million, what was its population in 2000?

7.  In 1994, Zaire’s per capita GNP was $125 (70% lower than it was in 1958).   What was Zaire’s per capita GNP in 1958?

8. You have a voucher for $20 to be used at a restaurant.  You will need to pay a 2% tax plus a 15% gratuity.  What is the most expensive entree you can buy?

9. The following table appeared in Investor's Business Daily in 2003:

It contains a major percentage mistake.  Find it and correct it.