Problem 12.
Plot the data set based on the first class letter postage for the US Mail from 1933 to 1996 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?
Here is the data set for first class letter postage from 1933 until 1996.
| 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 |
Here is a graph of the data created using Microsoft Excel.
Next, we will create a prediction function.
The function looks like a growth function in the form 
.
In this form, the x variable would be the year and the y variable
would be the rate.
After manipulating an equation of best fit, we come up with the equation
Here is the graph with the equation graphed in pink.
The cost of a first class postage stamp will reach 64 cents
in the year 2016 and over $1.00 in the year 2028.
According to our model, a three cent increase should have occurred
last year.