Question 282418: If your allowance was a penny doubled every day, how many days would it take for you to have over $1000.00? On which day would you have over %10000.00? how much money would you have on the 15th day?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! If your allowance was a penny doubled every day, how many days would it take for you to have over $1000.00? On which day would you have over %10000.00? how much money would you have on the 15th day?
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The total on the nth day is 2^n - 1 (cents)
For $1000 and $10,000 (I assume that's what you meant) ignore the -$0.01.
 in cents
n*log(2) = log(100000) = 5
n = 5/log(2) =~ 16.6 --> 17 days
2^17 = 131,072 = $1310.72
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Do the $10,000 the same way.
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An alternative is to look at the powers of 2, if you dont' know them.
$10,000 --> 1,000,000
A lot of people recognize that 1 Meg = 2^20, which is close to 1,000,000 and the 64K (of RAM, eg) = 2^16.
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1 Gig = 2^30 = 1073741824
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I don't know what 1 terabyte (2^40) is from memory.
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On day 15, you have 2^15 - 1 = 32767
= $327.67
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