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Math Help - looping

  1. #1
    mimi1980
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    looping

    hi, i cant figure out this equation and its making me nuts, a man gets 1 cent for the first day, it doubles everyday for 34 days................................next part, when would be become a millionaire?
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  2. #2
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    Quote Originally Posted by mimi1980 View Post
    hi, i cant figure out this equation and its making me nuts, a man gets 1 cent for the first day, it doubles everyday for 34 days................................next part, when would be become a millionaire?
    M= 1(2)^n where M is money (in cents) and n is number of days.

    So sub n = 34 and solve for M.

    Sub M = (however many cents are in one million dollars) and find the first integer valuem of n such that you've got at least a million dollars. Trial and error might be the best appoach here ..... Hint: From the first part you know n < 34 ......)
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  3. #3
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    Hello, mimi1980!

    A man gets 1 cent for the first day, it doubles everyday for 34 days.
    (a) How much will he have at the end of the period?
    (b) When would be become a millionaire?

    He gets: . 1 + 2 + 4 + 8 + 16 + \hdots + 2^{33} cents.

    This is a geometric series with first term 1 and common ratio 2.

    The sum is: . 2^{34}-1 \:=\: 17,179,869,183 cents.

    (a) He will have a total of: . \$171,798,691.83


    When does 2^n - 1 \:=\:100,000,000 cents?

    We have: . 2^n \:=\:100,000,001

    Take logs: . \ln(2^n) \;=\;\ln(100,000,001)\quad\Rightarrow\quad n\!\cdot\!\ln(2) \:=\:\ln(100,000,001)

    Hence: . n \;=\;\frac{\ln(100,000,001)}{\ln(2)} \;=\;26.5754...

    (b) He becomes a millionaire on the 27th day.

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, mimi1980!


    He gets: . 1 + 2 + 4 + 8 + 16 + \hdots + 2^{33} cents.

    This is a geometric series with first term 1 and common ratio 2.

    The sum is: . 2^{34}-1 \:=\: 17,179,869,183 cents.

    (a) He will have a total of: . \$171,798,691.83


    When does 2^n - 1 \:=\:100,000,000 cents?

    We have: . 2^n \:=\:100,000,001

    Take logs: . \ln(2^n) \;=\;\ln(100,000,001)\quad\Rightarrow\quad n\!\cdot\!\ln(2) \:=\:\ln(100,000,001)

    Hence: . n \;=\;\frac{\ln(100,000,001)}{\ln(2)} \;=\;26.5754...

    (b) He becomes a millionaire on the 27th day.

    So he keeps the money from each day ......? I assumed he only got whatever the money was on the final day ......
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