posted by Erica .
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?
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 -
Actually, that does not count the snap that starts the events. So, add 1, making 25 snaps.
Math - PPS -
Belay that prior comment
n 2^(n-1) - 1
So, 2^(n-1) = 31536001
n-1 = log2
so, there will be 25 snaps, but for a different reason.