Growth, Decay, Compound Interest Questions

(Spreadsheet Approach)
I chose this investigation because last year I introduced growth, decay and compound interest questions as a mathematical extension to a typically straight forward unit on exponents. I found that the students were able to handle the mathematics behind these questions but most of their understanding was procedure based and not conceptual. I would like to take a few of the questions from the quiz and answer them using the aid of a spreadsheet in hopes that it may present the material in a new or better way such that the concepts become clearer .
3 Questions from an Exponents Math Quiz, October 22nd, 1996

1. There were two ants in an ant hill, Adam and Eve Ant. One day there heard a loud voice from the depths of the earth say "Adam & Eve Ant multiply and replenish the ant hill!!". Adam and Eve followed the advice of the voice.

a) Actually the ant population began growing 4 times its previous size every 10 days. What was the size of the ant hill population after 370 days? (2 decimal places)

We begin with 2 ants and every 10 days we increase by 4 times, thus the simple muliplicative formulas.

The spreadsheet takes us away from exponential formulas and we can look at the growth that occurs every 10 days. I think this helps students understand how fast growth occurs when exponents are involved.

b) After that year, they heard the voice again but this time it said "There are too many ants in the ant hill. You must kill your first born of every family to level out the population." The ant families obeyed reluctantly, the ant hill population decreased 60% every 3 hours, what is the population after 6 days of killing? (2 decimal places)

This problem requires a little more thinking. The percentage is given concerning who dies, yet the question asks for who is living after the given time period thus the 60% represent the killed population, and the other 40% represents the living population. This information is seen in the formula used below.

 

2. Joe Smoe's parents placed $1000 dollars into a bank account on the day he was born. The account earned 5.75% interest compounded annually.

a) What will that be the amount in the account on his 65 birthday? (2 decimal places)

 Once again by setting up the basic relationships between the principal and the interest rate we see the year by year growth of ones investment. The formula shows how each year's money value is again multiplied by our constant growth rate of (1 + Interest Rate).

 

 

b) How much interest was earned in the 63rd year? (2 decimal places)

 

 

3. Jane Doe won the 1,000,000,000 dollar lottery. One of the conditions of this particular lottery is that Jane must spend exactly 10% each month of the cash that is currently in the account.

a) How much money did she have to spend in here first month?

10% of 1,000,000,000 is 100,000,000

b) How much money did she have to spend in her 76th month? (2 decimal places)

$36,998.85 was spent in her 76th month.

c) How many months would it take you till you have a value of less than ten dollars in the account?

In the 175th month the money value would be less then ten dollars.

The end!!!!