My Rich Aunt

You have a rich aunt who would like to put money away for you that you will get on your 15th birthday.  She has two options.  She could give you $1000 each year on your birthday starting on your 1st birthday or she can give you $1 on your first birthday, $2 on your second, $4 on your third (doubling the amount each year) and so forth

I think that having my aunt give me $1000 dollars every year for my birthday will end up giving me more money by my 15th birthday.

1.  Which method shows a constant rate of change? $1,000 each year

2.  Which method shows an exponential rate of change? Doubling each year.

3.  How much would you have from each method on your 13th birthday? $13,00 from the $1,000 year , and $354,348 from doubling each birthday.

4.  How much would you have from each method on your 15th birthday? $15,000 from $1,000 each year ad $3,189132 from the doubling each year.

5.  Explain what happens in those last two years to make one method better than the other.

6.  Does the method you chose in your prediction give you the most money on your 15th birthday?  Explain why or why not you are happy with your original prediction using mathematical terminology.  Man, we I wrong! The method that I choose was way less the other. I was not a happy camper when I found out that by my 15 birthday with the method that I choose I had about $3,000,000 less than the other method. That a lot of money!

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