Snap to It...
I snap my fingers now, in one second, I smap them again. I wait two seconds and snap them a third time. I wait 4 seconds before snapping them again. Then I wait eight, then sixteen, and the pattern continues. The interval between each snap doubles each time. How many times will I snap my fingers during the next year.
add them and then divide by two
see
http://www.jiskha.com/display.cgi?id=1334291563
The owner of a quick oil-change business charges $20 per oil change and has 40 customers per day. If each increase of $2 results in 2 fewer daily customers, what price should the owner charge (to the nearest $2) for an oil change if the income from this business is to be as great as possible?
To determine how many times you will snap your fingers during the next year, we need to calculate the total number of snaps based on the given pattern. Let's break it down step by step:
First, let's find out how many snaps you make in each doubling interval. You start with 1 second, then 2 seconds, 4 seconds, and so on. Each doubling interval represents a power of 2. Let's represent the doubling intervals using the exponent of 2:
1st interval: 2^0 snaps (1 second)
2nd interval: 2^1 snaps (2 seconds)
3rd interval: 2^2 snaps (4 seconds)
4th interval: 2^3 snaps (8 seconds)
5th interval: 2^4 snaps (16 seconds)
and so on...
We can see that the number of snaps doubles with each interval, given by 2 raised to the power of the interval number.
Now, let's calculate how many intervals there are in a year. Considering that a year has 365 days and each day has 24 hours, we can calculate the total number of hours in a year:
365 days/year × 24 hours/day = 8760 hours/year
Since each doubling interval doubles the amount of time, we can calculate the number of intervals in a year by dividing the total number of hours (8760) by the initial doubling interval time (1 second or 1/3600 hours):
8760 hours/year ÷ (1/3600 hours) = 31536000 intervals/year
Finally, to find the total number of snaps during the next year, we sum up the number of snaps in each interval:
Total snaps = 2^0 + 2^1 + 2^2 + 2^3 + 2^4 + ... + 2^31536000
Calculating this sum is beyond the capabilities of a regular calculator or even most computers due to the immense magnitude of the number. However, we can conclude that over the course of a year, you will snap your fingers an astronomical number of times.