This data set is based on the first class letter postage for the US Mail from 1919 to 2002.
I will be using, for my x values, the years since 1919. Here is a table that displays this data.
|years since 1919||rate(in cents)|
We can use excel to plot the data and develop a prediction function.
We can tell from this graph, that the rate appears to be an exponential function.
We can use the Chart Wizard in Excel to create and graph a function that will represent the curve otoan exponential function.
We can see that chart wizard has found the exponential function equation to be
The set of data generated by this equation has a variance of 8.7564. Variance is found by taking the average of the squares of teh differences between the original data and the data generated by using the function that estimates the curve. For a perfect fit, variance would be zero.
We can generate our own exponential equation to model the curve. The equation of the curve would take the form of y = ae^bx.
Since the cost of the stamps in the first year was $0.02, or 2 cents, a should be 2. What value of b should we try?
By comparing the ratios, b should be a number close to .03, this is close to the value for b that excel suggested, so I tried values between .0397 and .03
The value for b that came the closest to modeling the curve was .0356
Using a = 2, and b = .0356 the equation for the curve would be
The set of data generated by this equation has a variance of 8.257
Because 8.257 is closer to zero than 8.7564, this equation comes much closer to modeling the curve than the one that excel suggested.
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?
Using our equation, we can answer these questions.
The cost of stamps will reach $ 1.00 110 years after 1919, so we can expect the cost of stamps to be $ 1 in 2029.
The cost of stamps will reach $0.64 97 years after 1919, so we can expect the cost of stamps to be 64 cents in 2016.
The next time that the cost of stamps will increase by 3 cents will be in 2025 when the cost will go from 84 cents to 87 cents.
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