# Exponential Growth Activity

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```							Name ________________________________                             Date ___________________

Exponential Growth Activity
Imagine two people, Ashley and Bobby. They both have some extra money that they want to
invest in a bank and try to earn some interest. Ashley has \$5,000 to invest, and her bank
account offers her a 3% interest rate, compounded monthly. Bobby only has \$3,000 to invest,
but his bank offers him a 4% interest rate, compounded quarterly. Let’s investigate these two
bank accounts a little!

Problem #1: Write a formula to find the amount of money in each of their accounts after 15
years.

Ashley’s account: ________________________ Bobby’s account: ________________________

Problem #2: Who has more money after 15 years, according to those two above formulas? Did
you expect that? Why or why not?

Problem #3: Write a formula to find the amount of money in each of their accounts after 50
years.

Ashley’s account: ________________________ Bobby’s account: ________________________

Problem #4: Who has more money after 50 years, according to those two above formulas? Did
you expect that? Why or why not?

Problem #5: Use the above information to write a formula to find the amount of money in
each of their accounts after x years. (Think about where the variable belongs in the formula;
everything else should remain the same!)

Ashley’s account: ________________________ Bobby’s account: ________________________

Problem #6: How could this have happened? Can you explain how this is even possible?
So we’ve discovered that, even though Bobby started with less money than Ashley, he can
eventually have more than her. So here’s the ultimate question: How long will it take for
Bobby’s account to have more money in it than Ashley’s account?

The two formulas that you came up with in problem #5 are pretty nasty-looking! We can’t
solve an equation that looks like that (yet….), so we need an idea to help us solve this question.
Maybe we can use the graphs to help…

STOP! Don’t read any further! Head on over to the GeoGebra activity and check out the graphs.

Okay, so now you’ve seen what the graphs look like and have had a chance to play with them.
Answer the last few questions below:

Question #1: How long will it take for Bobby to have more money than Ashley?

Question #2: How did you use the graphs to determine that point?

Question #3: Based on this activity, what is the most important part of an investment in a bank
account: the principle, the interest rate, or the compounding interval? Why?

Question #4: If you had some money to invest and were offered a 3% interest rate,
compounded once per second, or a 5% interest rate, compounded annually, which should you
take? Why?

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