## USING SPREADSHEETS

#### by

### Angie Head

We can use Excel or other spreadsheets to explore many different types of
problems. For example, we can explore growth and decay problems, interest
compounded problems, any kind of statistical problem, and many more. In
this paper, I am going to use Excel to perform two different types of problems.
I am going to predict the size of a population of a species in the year
2050 and I am going to perform an interest compounded problem.

**Population growth**

Hypothetical problem: Suppose that there is a species in the rain forest
of Brazil that has a population of 8,000,000 in 1960 and that it increases
at a rate of 5 percent every five years. What will the population be in
2050?

We know that the formula for finding the population of a species is

Q=Q(0)e^k(t-t(0))
where Q(0) is the starting population, k is the rate, t(0) is the starting
year, t is the year that you desire to know the population of, and Q is
the desired population. Thus, in our problem, Q(0)=8,000,000, t(0)=1960,
t=2050, and k=.05. The following Excel spreadsheet calculates Q every five
years.

From this excel worksheet, you see that for the year 2050 the population
will be 720137050.4. This is an astonishing number, but there are many factors
that will affect the population that are not accounted for in this formula.
For example, this number does not account for the deaths of this species
bewteen these years. Thus Q, is not actually correct. To find a better estimate
for this population, you would need to account for the deaths of this species
and any other factor that might attribute to a change in population of this
species.

**Interest Compound **

Hypothetical problem: Suppose that you want to buy some furniture for
your apartment, but the only way that you can buy it is to charge it on
your credit card. You have been looking around getting estimates of the
furniture that you want. Now, you want to see what will be the best purchase
for your budget. Suppose that the interest rate on your credit card is 18.15%
and you know that your credit card is compounded continously. What will
be the gross total of your furniture and what will the payments be if you
want to pay your bill off in one year?

We are going to use the following formulas to help us in our calculations.

G=pe^(rt),
where G is the gross total, p is the principal, t is the time, and r
is the interest rate.

This formula finds your gross total if your interest is compounded continously.

To find the amount of interest on your purchase, we use the formula

I=G-p
where I is the amount of interest, p is the principal, and G is the gross
total.

To find the amount of the payments, we used the formula

A=G/n
where A is the amount of payments, G is the gross total, and n is the
number of payments.

We obtain the following spreadsheet:

By observing the above spreadsheet, you are able to determine the best
purchase for your budget.

One can use spreadsheets to solve many problems. The ones above are only
two of the types of problems that can be solved using spreadsheets.

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