On day 1 you will receive 2^0 = 1 penny
On day 2 you will receive 2^1 = 2 pennies (total = 3)
On day 3 you will receive 2^2 = 4 pennies (total = 7)
...
On day n, you will receive 2^(n-1) pennies for a total of 2^n - 1 pennies.
So if you want this for 30 days, plug in n = 30.
On day 30, you will receive 536,870,912 pennies ($5.4 million), for a total of 1,073,741,823 pennies ($10.7 million)
Edit:
I see you have restated your question elsewhere. The question is, on what day would you be a millionaire. Same question if you had nickels instead of pennies.
You want to figure the day when 2^n - 1 is greater than or equal to 100 million coins (= $1 million).
2^n - 1 >= 100,000,000
2^n >= 99,999,999
Take the log base 2 of both sides.
n = log_2(99 999 999)
log(99 999 999) / log(2) = 26.5754247
27 days to be better than a millionaire with pennies.
The same logic for the nickel, but this time you only need 20 million nickels to make you a millionaire.
2^n - 1 >= 20,000,000
2^n >= 19,999,999
n = log_2 (19,999,999)
log(19 999 999) / log(2) = 24.2534966
25 days to be better than a millionaire with nickels.
2007-10-29 09:12:31
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answer #1
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answered by Puzzling 7
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The question seems to have been cut off, but if you're asking how many cents you'll have on a certain date, the answer is 2^n - 1, where n is 1 for January 1, 2 for January 2, etc.
2007-10-29 16:13:10
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answer #2
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answered by Ian 3
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