The following problems are meant to generate discussion of how to apply linear models to real problems. These kinds of questions should be answered in complete sentences providing (1) an accurate description of the model to be used and how it was found (e.g., did you plot the data and "eyeball" it or something else?) and (2) answers to the questions asked presented with proper grammar and units.

1. (Source: 1996, W. Marsh, Environmental Geography, John Wiley & Sons) Since 1950, the total daily water use in the U.S. has been increasing by roughly 80 billion gallons every ten years. (The U.S. used approximately 200 billion gallons per day in 1950.) Let w_n be the daily water usage (in billions of gallons) in the year n years after 1950. For example, w₀ is the daily water use in 1950 which is given as 200.
1. Find the difference equation suggested by the above description of arithmetic growth. (This equation is your model of the problem.)
2. Find the functional equation that corresponds to your difference equation.
3. Use your model to predict the amount of daily water usage in the year 2000.
4. In what year does your model predict that the daily water usage surpassed 500 billion gallons/day for the first time?
2. (Source: The Wall Street Journal, June 10, 1998) The average hourly pay of production workers in the private business sector has risen $0.45 each year since1995 (at which time it was $11.55/hour).
1. Find the difference equation suggested by the above description of arithmetic growth. (This equation is your model of the problem.)
2. Find the functional equation that corresponds to your difference equation.
3. Use your model to predict the average hourly pay of production workers in the year 2000.
3. (Source: Advertisement, Newsweek, June 15, 1998) According to a paid advertisement advocating Social Security reform, the total amount of money paid into Social Security in 1995 was 250 billion dollars, and the prediction is that this amount will grow by 80 billion dollars each year into the near future.
1. Find the difference equation suggested by the above description of arithmetic growth. (This equation is your model of the problem.)
2. Find the functional equation that corresponds to your difference equation.
3. The advertisement predicts that in the year 2032, Social Security will not take in enough to pay full benefits. Use your model to predict the total amount of money taken in by Social Security in the year 2032.  (We will see later how to model the expenditures by Social Security.)
4. (Source: "Women gaining in wage gap," Associated Press), June 9, 1998) In the 12 months ending March 31, the median weekly wage for women working full time grew from $427 to $455 while the median weekly wage for men working full time grew from $582 to $596.
1. Find functional equations for two lines, one that describes the median weekly wage for women and the other describing the median weekly age for me. (These equations are your model of the problem.)
2. Use your model to predict the median weekly wage for each sex in the year 2000.
3. In what year does your model predict that women and men will have the same median weekly wage? Do you believe this?
5. (Source: "What really ails Russia," Newsweek, June 8, 1998) The following table provides some data about the value of the Russian ruble over the first five months of this year.

Month	Jan.	Feb.	Mar.	Apr.	May
Number of rubles in $1 (US)	6.00	6.05	6.10	6.13	6.18

 
1. Find a functional equation for a line that "fits" this data well. (This equation is your model of the data.)
2. Use your model to predict the number of rubles per U.S. dollar in June.
3. According to your model, how long ago was the exchange rate 5 rubles per dollar? Do you believe this?
6. (Source: USA Today, June 9, 1998) The following chart summarizes the number of personal bankruptcies (in millions) for several years:

Year	1980	1985	1990	1995	1997
Bankruptcies (millions)	0.3	0.4	0.7	0.9	1.3

 
1. Find a functional equation for a line that "fits" this data well. (This equation is your model of the data.)
2. Use your model to predict the number of personal bankruptcies in the year 2000.
3. In what year does your model predict that the number of personal bankruptcies will first exceed 2 million?