Stamp
Problem

#### by

#### Rachael Brown

To solve this problem, I used an Excel spreadsheet.
I put the data in and then graphed it. I used my experience with
graphs to choose a model. I decided the graph looked like an exponential
growth curve.

Here is what the graph of the data looks like:

I first explored the model given that
the postage doubled every 10 years. To model this, I used the
equation
This shows that we started at two cents and
double. To make sure we were doubling every 10 years, I took the
year and subtracted it from 1919 (the start year) and then divided
by ten. That let me know how many decades had passed. Here is
this model graphed with the original data. The model is in pink.

As you can see, this is a terrible model! This
lead me to believe that the growth factor of the correct model
had to be less than two. After spending some time guessing and
checking, I felt comfortable with the following model:

Here is the picture of my model and the given
data:

The original data is blue and my model is pink.
As you can see it isn't perfect but it does a much better job
than the previous model.

To answer when will the cost of a stamp reach
$1.00, we need to plug into our model formula and solve. Remember
our y is in cents and the x is the year, so we need to plug 100
in for y.

Thus, in 2032 a stamp should cost $1.00 according
to my model.

To determine when the cost will be 74 cents,
we need to plug 74 in for y.

Thus, the cost of stamp should be 74 cents
in 2023.

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