SOLUTION: Please help me solve this problem: Joe decided to start a penny collection. He starts his collection with one penny on the first day, then two pennies on the second day, then

Click here to see ALL problems on Linear Equations And Systems Word Problems

Question 1041582: Please help me solve this problem:

Joe decided to start a penny collection. He starts his collection with one penny on the first day, then two pennies on the second day, then four pennies on the third day, and then eight pennies on the fourth day.
Assume this pattern continues and determine the total size of Joe's penny collection on the 15th day.
Fill in the Blank:
If Joe continues with this pattern, he will have _____ pennies on the 15th day.

Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Joe decided to start a penny collection. He starts his collection with one penny on the first day, then two pennies on the second day, then four pennies on the third day, and then eight pennies on the fourth day.
Assume this pattern continues and determine the total size of Joe's penny collection on the 15th day.
---------
Use days 0 to 14:
Day 0 - 1
Day 1 - 2
day 2 - 4
.
.
.
Day 14 - 16384 (2^14)
=======================
Add them --> 2^15 - 1
= 32767 pennies.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The number of objects collected starting with 1 on the first day and doubling each day thereafter for a total of days is given by:

So at the end of 15 days, he will have pennies.

And, if he were able to keep up the pace for the entire 30 day month, he would have saved up a tidy nest egg of $10,737,418.23.

John

My calculator said it, I believe it, that settles it