If your allowance was a penny doubled every day, how many days would i

1.	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 $10 000.00? How much money would you have on the 15th day?
Answer» Answer: Step-by-step EXPLANATION: 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. 2%5En+=+100000 in cents *nlog(2) = log(100000) = 5 n = 5/log(2) =~ 16.6 --> 17 days 2^17 = 131,072 = $1310.72 Do the $10,000 the same way. 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. ------------------------------ 1 Gig = 2^30 = 1073741824 --------------------------- I don't know what 1 terabyte (2^40) is from memory. ------------ On day 15, you have 2^15 - 1 = $327.67**

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 $10 000.00? How much money would you have on the 15th day?

Answer»

Answer:

Step-by-step EXPLANATION:

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.

2%5En+=+100000 in cents

n*log(2) = log(100000) = 5

n = 5/log(2) =~ 16.6 --> 17 days

2^17 = 131,072 = $1310.72

Do the $10,000 the same way.

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.

------------------------------

1 Gig = 2^30 = 1073741824

---------------------------

I don't know what 1 terabyte (2^40) is from memory.

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On day 15, you have 2^15 - 1 = $327.67