Assignment 12 Problem # 12
The spreadsheet is a utility tool that can be adapted to many different explorations, presentations, and simulations in mathematics. There are spreadsheets available on almost any platform. An essential feature should be the ability to make graphs and charts from the matrix of data. Try using a spreadsheet, such as EXCEL, WINGS, or ClarisWorks, for some of the following investigations.
This data set is based on the first class letter postage for the US Mail from 1933 to 1996. Plot the data and develop a prediction function. When will the cost of a first class postage stamp reach $1.00? when will the cost be 64 cents? how soon should we expect the next 3 cent increase?
Before I begin my exploration of the cost for stamps in the coming years, I must give some background information on stamps. Here is a list of the prices of stamps since 1919:
year  rate(in cents) 
1919  2 
1932  3 
1958  4 
1963  5 
1968  6 
1971  8 
1974  10 
1975  13 
1978  15 
1981  20 
1985  22 
1988  25 
1991  29 
1994  32 
This problem really baffled me from the beginning because I have never looked at this problem in a way that Dr. Wilson has asked it (in fact, many of the problems he has given us have been based on real world applications  and I feel weird about the problems sometimes because I will say to myself on some occasions that I can't do it...when I can...but I just don't push myself hard enough....).
Anyway, this problem, looks at postage prices and the years in which the value has increased. There are several ways to look at this problem...let's look at it the way I viewed it in the beginning....that is...the wrong way:
Now click here to look at the spreadsheet appropriately titled "The Wrong Stamps Stamps Stamps" so that you may see how I tried to interpret this information...what's wrong with the information presented in the datat? Why? How or what could be done to fix the data?
Here is a new spreadsheet that I put together that includes all the years beginning with 1919 and ending in the year 2000 (assuming that the year 2000 does not have any increase in the value of the stamp).
year  rate (in cents) 
1919  2 
1920  2 
1921  2 
1922  2 
1923  2 
1924  2 
1925  2 
1926  2 
1927  2 
1928  2 
1929  2 
1930  2 
1931  2 
1932  3 
1933  3 
1934  3 
1935  3 
1936  3 
1937  3 
1938  3 
1939  3 
1940  3 
1941  3 
1942  3 
1943  3 
1944  3 
1945  3 
1946  3 
1947  3 
1948  3 
1949  3 
1950  3 
1951  3 
1952  3 
1953  3 
1954  3 
1955  3 
1956  3 
1957  3 
1958  4 
1959  4 
1960  4 
1961  4 
1962  4 
1963  5 
1964  5 
1965  5 
1966  5 
1967  5 
1968  6 
1969  6 
1970  6 
1971  8 
1972  8 
1973  8 
1974  10 
1975  13 
1976  13 
1977  13 
1978  15 
1979  15 
1980  15 
1981  20 
1982  20 
1983  20 
1984  20 
1985  22 
1986  22 
1987  22 
1988  25 
1989  25 
1990  25 
1991  29 
1992  29 
1993  29 
1994  32 
1995  32 
1996  32 
1997  32 
1998  33 
1999  33 
2000  33 
and here is the the graph for the above spreadsheet:
So I had to ask myself at this point, what now? Where do I go from here?
Should I continue the graph as I did in the Wrong Stamps graph, or should I look at the function in and among itself to figure out what the value of the stamps may be in the coming years? I think that maybe I will try to look for some function to see if there is some correlation between the value and the years.
Let's look at something interesting that I found:






























































If you look at the amount of increase for the years that are corresponding, you will notice that the cost (in cents) + the amount increase in value = the next level's cost (in cents). Does this mean anything? Did I just look at this in the wrong way? I have no clue, but I will continue my search...