for

Shanti Howard

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:

 Actual Year Of Stamps # of Years in between Cost (in cents) Amt increase in value for each level (or step) 1919-1932 13 yrs 2 1 1932-1958 26yrs 3 1 1958-1963 5yrs 4 1 1963-1968 5yrs 5 1 1968-1971 3yrs 6 2 1971-1974 3yrs 8 2 1974-1975 1yr 10 3 1975-1978 3yrs 13 2 1978-1981 3yrs 15 5 1981-1985 4yrs 20 2 1985-1988 3yrs 22 3 1988-1991 3yrs 25 4 1991-1994 3yrs 29 3 1994-1999 5yrs 32 1 1999-Present 33

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...