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?"
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