January 7, 2006
The Ever-changing Price of a U.S. Postage Stamp
by Margaret Trandel
In this assignment I used Excel to record the price of the U.S. postal stamp from 1919 to 2006. How apropos that I am working on this assignment today, as at midnight tonight the price jumps to from .37 to .39 to mail a first class letter! Thank goodness for e-mail, or all of us would go broke!
Using Excel, I will find a regression equation and make predictions to answer the following questions:
When will the cost of a first class postage stamp reach $1.00?
When will the cost be .64?
How soon should we expect the next 3 cent increase?
The table below shows stamp prices from 1919 to January 8, 2006
Below is a scatter plot of the stamp data. As you can see, the data appears to fit an exponential model. In an exponential model, as x becomes larger, y continues to increase at a growing rate. This fits our model. For example, between 1919 and 1958, stamp prices only increased by two cents, and in the past two years alone stamp prices have gone up by two cents! The years in between for the most part reflected increases at an overall growing rate.
To find our exponential equation of best-fit, we can use the TI-83 Graphing Calculator or Excel. Since I am familiar with the graphing calculator method, I decided to learn about the Exce graphing and regression features. Below you will find the Excel Scatterplot, Exponential Equation of Best Fit, and and the graph of the Exponential Equation.
The equation for our data (for price in dollars) is:
y = 2E-35e^.0394x
Let's use this equation to predict future stamp prices. I made a new chart below and included the predicted postage rates through the year 2028, when stamp prices reach a dollar according to the model.
As you can see, based on this model the price of a stamp will reach $1.00 in 2028. The cost will be .64 around 2017, and we can expect the next 3 cent increase this year? ??? We'll all have to stay tuned to see what happens...and in the meantime, make sure to remember to purchase some of these at the post office this week!