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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. 