Homework Help: Math

Posted by Erica on Tuesday, March 13, 2012 at 7:21pm.

I snap my fingers now. in one second, i snap them again. I wait two seconds and snap them a third time. I wait four seconds before snapping them again. then i wait eight seconds, then sixteen, and the pattern continues on. the interval between snaps doubles each time How many times will i snap my fingers during the next year?

Math - Steve, Wednesday, March 14, 2012 at 10:25am
seconds in a year = 31,536,000
After n snaps, Sn = 2^n - 1 seconds have passed.

So, what is log₂31536000?
That is 24.9

So, there will be 24 snaps in the year.
25 snaps would require 2^25 = 33554432 seconds.
Math - PS - Steve, Wednesday, March 14, 2012 at 10:27am
Actually, that does not count the snap that starts the events. So, add 1, making 25 snaps.
Math - PPS - Steve, Wednesday, March 14, 2012 at 10:30am
Belay that prior comment
snaps seconds
1 0
2 1
3 3
4 7
5 15
n 2^(n-1) - 1

So, 2^(n-1) = 31536001
n-1 = log₂

so, there will be 25 snaps, but for a different reason.
Math - Erica, Wednesday, March 14, 2012 at 4:44pm
thanks steve

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