Stamps
Consider the following data set of first class
postage stamp prices over the past several decades.
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 
1997 
33 
1999 
34 
2002 
37 
It would be useful to use this data to form
some predictions of what stamp prices will be in the future. A spreadsheet is an
ideal tool for accomplishing this task. After entering this data into a
Microsoft Excel spreadsheet, we can use Excel's chart capabilities to create a
scatterplot of stamp prices as a function of year to get a feel for what the
data looks like.
The spread of the data strongly suggests an
exponential relationship between the price of stamps and the year. Excel has a
built in function that allows the user to fit a trendline or curve to the data.
The user can specify an equation or the user can let Excel select the
"best fit" for a certain kind of equation. We've hypothesized that an
exponential equation would be a good fit for the data.
So we have used Excel to fit a curve with the
equation y=1E33e^{0.00397x}. Looking at the chart, this seems like a
reasonable fit.
Now we have a few ways we can use this chart to predict the future. We can use Excel to use the trendline equation to forecast the next x units. Then we can visually look and estimate our predictions.
So if we wanted to predict when the price
would be 64 cents we could look at our curve and say that that would be the
price sometime around 2018. If we wanted to predict when the price would be one
dollar, we could look and estimate that it would be around 2027.
If we wanted to be more precise in our predictions, we could use the trendline equation to calculate our predictions directly or by typing it into Excel as a formula.
year 
Predicted price (in
cents) 
2015 
55.157 
2016 
57.391 
2017 
59.716 
2018 
62.134 
2019 
64.650 
2020 
67.268 
2021 
69.993 
2022 
72.827 
2023 
75.777 
2024 
78.846 
2025 
82.039 
2026 
85.361 
2027 
88.818 
2028 
92.415 
2029 
96.158 
2030 
100.052 
2031 
104.104 
2032 
108.320 
2033 
112.707 
2034 
117.272 
2035 
122.021 
I created this table by typing in our prediction equation in the cells in the Predicted price column. The price is calculated according to the year in the corresponding cell in the year column. So we predict from this table that a stamp will cost 64 cents sometime between 2018 and 2019. We can then go on and predict that a stamp will cost 1 dollar sometime around 2030.