Question

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 1

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.

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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 = $327.67

Answer 2

Answer:

1. 20 days
2. 30 days
3. 327.67

Step-by-step explanation: