Making a mathematical formula using exponents

J

JayCee

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Oct 2, 2007
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Ok, my teacher had us do this assignment where if you got 1 penny on day one, and it double from there, 2 pennies on day 2, 4 pennies on day 3, 8 pennies on day 4, etc. He had us do this up to day 28 or 28 days in a month. I then figured out the answer for 28 days in a month, which comes out to being $134,217,728. After that, he wanted us to make a mathematical formula using exponents to determine this answer for the 28 day total.

However, i'm having trouble figuring out how to do this. All the steps I have taken and tried aren't equaling out to the total that I have for the 28 days.. If anyone can help me with this and show me the way/formula on how to do it, I would greatly appreciate it. Thank you so much everyone, i'm just trying to increase my skills in this part of algebra that i'm having trouble in. Thanks again.
 
t----amount------total sum
1----1 or 2^0-----1or 2^1-1
2 ---2 or 2^1-----3 or 2^2-1
3----4 or 2^2-----7or 2^3-1
4----8 or 2^3-----15 or 2^4 -1
--------
n---- 2^(n-1)

the amount of pennies on day n is 2^(n-1)
the total amount is 2^n -1

Arthur
 
Thanks Arthur for the reply.

He wants a mathematical formula using exponents that solve for the 28 day amount. So i'm trying to figure out a formula that will give me the total amount of the pennies double for the 28 days, which is the $134,217,728. But I see what you did for the day to day basis, which is perfectly fine thank you. I just wanna figure out a problem that will give me that grand total for the 28 day month.
 
JC, what are you asking? Arthur gave you the formulas!

2^(n-1) = 2^(28-1) = 2^27 = 134,217,728 : on 28th day

2^n - 1 = 2^28 - 1 = 268,435,455 : days 1 to 28
 
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