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 scatter-plot 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=1E-33e0.00397x. 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.