Problem: The following data is based on the first class
letter postage for the US Mail from 1933 to 2002. Can you believe stamps used
to cost 2 cents? 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? All of these
questions can be answered by finding the best fit equation. This graph looks like
an exponential growth, y = a b^{x}, where x will be the year and y will
be the rate.
Now, how can
this exponential equation help answer those previous questions? Let’s
look at a spreadsheet with some additional values.
Year 
Rate (in cents) 
Exponential Equation 



1919 
2 
1 
1932 
3 
2 
1958 
4 
6 
1963 
5 
8 
1968 
6 
10 
1971 
8 
11 
1974 
10 
12 
1975 
13 
13 
1978 
15 
14 
1981 
20 
16 
1985 
22 
19 
1988 
25 
21 
1991 
29 
24 
1994 
32 
27 
1997 
33 
30 
1999 
34 
33 
2002 
37 
37 
2004 
? 
40 
2006 
? 
43 
2008 
? 
46 
2010 
? 
50 
2015 
? 
61 
2016 
? 
64 
2025 
? 
91 
2026 
? 
95 
2027 
? 
99 
2028 
? 
103 
From this table of values we can predict the next 3 cent increase
to occur next year. Stamps will cost 64 cents in 2016 and over a dollar in
2028!! We will have to wait and see how accurate our prediction model is.