Please help me with this math problem?
Receive a penny on January 1st, two cents the next day, four cents the next day, and so on, doubling every day. How long will it take to become a millionaire? Suppose you started with a nickel and doubled, how long before you are worth a million dollars?
On day 1 you will receive 2 ^ 0 = 1 coins to 2 days you will receive 2 ^ 1 = 2 coin (total = 3) On day 3 you will receive 2 ^ 2 = 4 coins (total = 7) On day 4 you will receive 2 ^ 3 = 8 coin (total = 15) ... In general, the n days, you will receive 2 ^ (n-1) for coins a total of 2 ^ n - 1 coins. Want to know the day when the accumulated value (2 ^ n - 1) is greater than or equal to 100 million coins (100 million pennies = 1 million dollars). 2 ^ n - 1> = 100,000,000 2 ^ n> = 100000001 Take the log base 2 of the parties. N = log_2 (100,000,001) log (100,000,001) / Log (2) = 26,5754248 n> = 26,5754248 days 27 days to be better than a millionaire with pennies. The same logic for nickel, but the time it need only 20 million Nickels to make you a millionaire. 2 ^ n - 1> = 20000000 2 ^ n> Log_2 n = 20,000,001 (20,000,001) log (20,000,001) / Log (2) = 24,2534967 n> = 24,2534967 25 days to be better than a millionaire with Nickels.
Bulls @ Knicks - 1995. Jordan's 55 point comeback
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