SOLUTION: You receive a penny on Jan 1, 2 cents the next day, 4 cents the next day and so on, doubling every day. How long will it take to be a millionaire?

Algebra ->  Decimal-numbers -> SOLUTION: You receive a penny on Jan 1, 2 cents the next day, 4 cents the next day and so on, doubling every day. How long will it take to be a millionaire?      Log On


   

Question 416486: You receive a penny on Jan 1, 2 cents the next day, 4 cents the next day and so on, doubling every day. How long will it take to be a millionaire?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
A millionaire has a least $1,000,000.00 and this is 100,000,000 pennies.
If you receive one penny on the first day then two on the next, four on the next, etc, doubling every day, the total number of pennies (T) acquired after n days can be expressed by:
T+=+2%5En+-+1 Substitute T = 100,000,000
100000000+=+2%5En+-+1 Solve for n. Add 1 to both sides.
2%5En+=+100000001 Take the logarithm of both sides.
Log%282%5En%29+=+Log%28100000001%29 Apply the power rule to the left side.
nLog%282%29+=+Log%28100000001%29 Divide both sides by Log%282%29.
n+=+Log%28100000001%29%2FLog%282%29 Evaluate using your calculator.
n+=+26.5754days.
So you would become a millionaire in 27 days!