Assignment #12

When will it cost me a dollar to send a letter?

By: Elizabeth Gore

Predicting the price of stamps could seem to be an unattainable goal, but that is not necessarily true.

With the miricle of mathematics we can use previous data to predict a trend. Let's begin with a chart of data.

Above is shown the price of a stamp to the corresponding year from 1919 to 1994.

To make our calculations easier, I will alter the chart to reflect the number of years since 1900.

For example, instead of using 1963, we will call our variable, n, 63.

It will give us a better understanding of the trend our data follows if we look at a scatter plot of the chart.

What do you notice about the curve? It appears to be exponentially increasing.

Let's chack and see if it follows a common function.

It seems to be pretty close to the function

but it is not exact.

What could we do to make this trendline more exact?

If we look closely we can see that the first two data points seem to lie outside of a curve that the other data points do.

So, let's ignore those and see if we get a more accurate curve.

Here is the data with the trend curve

Interesting we get a completely different equation for this trendline, and it follows much closer to the actual data.

Now that we know what equation our trend follows we can calculate the price of a stamp and when.

Here is our equation

Price of stamp =

Let's do some calculation.

When will the price of a stamp be \$1.75?

Set the "price of stamp" to be 175 and solve for x.

So, what does this mean. Well, it means that 118.844 yeas from 1900, the price of a stamp will be \$1.75. After eouding the number we get...

In approximately 2019, the price of a stamp will be \$1.75. Wow!!

Let's calculate and see if the price of a stamp today matches the prediction equaiton.

To do this, we will set the price of the stamp at \$.35

Here we see that the price reached 35 cents later than predicted with this equaiton.

This is because we eliminated some of our data to get the new equation.

I have used Excel to acquire the trend equations and prduce the charts and graphs.

Now that you know that this can be done, an interesting investigation for you would be to

figure out if the price of a stamp today closer matches the estimation given by the first equation.

Try answering the question in the title of this write-up, "When will it cost me a dollar to send a letter?"