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
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
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.
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
where I is the amount of interest, p is the principal, and G is the gross
To find the amount of the payments, we used the formula
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.