Functions Defined by Data

Part 1. First Class Postage Rates

The following is a list of first class postage rates (in cents) for more than a century.  Each rate is paired with the year in which it took effect.  Enter this data set.

postage  = 
       { {1885, 2},  {1917, 3},  {1919, 2},  {1932, 3},  {1958, 4}, 
         {1963, 5},  {1968, 6},  {1971, 8},  {1974, 10},  {1976, 13}, 
         {1978, 15},  {1981, 18},  {1982, 20},  {1985, 22},  {1988, 25}, 
         {1991, 29},  {1995, 32},  {1998, 33} }

Mathematica Tip.  If you don't want the data printed when entering a data set, put a semicolon at the end of the input cell.  This suppresses the display of the output.

Each data point is a pair of numbers (year and postage rate) enclosed within curley brackets { }, and the full list of data points is itself enclosed in an outer set of curley brackets { }.   This is a "list of lists," a good format for plotting data.  We create a scatter plot of the data by using the Mathematica ListPlot command.  Enter the following command.

ListPlot[postage,  AxesOrigin -> {1885, 0}]

See what happens with the PlotJoined->True option by entering the next line.

ListPlot[postage,  AxesOrigin -> {1885, 0},  PlotJoined -> True]

With the Prolog->AbsolutePointSize[d] option, if you want a different representation of the points, you can change the value of d, the diameter of the points.

ListPlot[postage,  AxesOrigin -> {1885, 0},  
      Prolog -> AbsolutePointSize[6]]

Write a brief description of what you learn from the graph about postage costs in the United States.  Type your comments here.  
Answer:

Part 2. The Spread of AIDS

The list AIDS, defiined below, contains the total numbers of AIDS cases reported to the Centers for Disease Control as of the dates indicated by numbers of months from the start of 1980.  Enter the AIDS data.

AIDS  = 
       { {20, 110},  {21, 129},  {24, 220},  {26, 257},  {29, 439}, 
         {31, 514},  {35, 878},  {37, 1029},  {41, 1756},  {44, 2057}, 
         {49, 3512},  {52, 4115},  {59, 7025},  {62, 8229}, 
         {67, 12067},  {69, 14049},  {73, 16458},  {83, 28098}, 
         {89, 36058},  {98, 56575},  {119, 113891},  {143, 202843}, 
         {151, 226252} }

Plot the AIDS data by completing and entering the following command.

ListPlot[?? ?]

ListPlot[AIDS,  PlotJoined -> True]

Write a brief paragraph about the AIDS epidemic graph.  
Answer:

Part 3. Federal Budget Deficits

Construct a data set "deficit" (much like "postage" and "AIDS") which contains the information from the Federal deficit table.  Edit and enter the following command.

deficit  =  ?? ?

Plot the data below.

ListPlot[?? ?]

What do you think about the "million dollars a day" claim in 1992?

Write a brief description in words of what you see in the deficit graph.  What do you learn from the table or the graph that you did not know before?  Type your response below.

Part 4. The Federal Debt

Estimate the total Federal debt at the start of 1993.  Type and Enter your calculations here.

Enter your calculations for percentage increase in the debt here.

Enter your calculations for interest paid on the debt here.

Enter your calculations for interest paid per capita here.