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Math Help - Find Bacteria After x Hours

  1. #1
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    Find Bacteria After x Hours

    If bacteria double in number every hour, how many bacteria will there be after x hours? Start with 1 bacteria?

    MY WORK:

    Let B = bacteria

    Is the equation B = 2^(x) + 1?

    Is this correct?
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  2. #2
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    Each hour the number of bacteria will double.

    Let B_i represent the number of bacteria at hour i. If there are n bacteria to begin with...

    Then

    B_0 = n

    B_1 = 2n

    B_2 = 4n = 2^2n

    B_3 = 8n = 2^3n

    B_4 = 16n = 2^4n.


    So what do you think B_x is?
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  3. #3
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    Quote Originally Posted by fdrhs1984 View Post
    If bacteria double in number every hour, how many bacteria will there be after x hours? Start with 1 bacteria?

    MY WORK:

    Let B = bacteria

    Is the equation B = 2^(x) + 1?

    Is this correct?
    Unfortunately, this does not even satify the "initial condition". If you started with 1 bacteria, then you should have B(0)= 1 but 2^0+ 1= 1+ 1= 2, not 0. Perhaps you were making the mistake of thinking that 2^0= 0 and added the "1". Drop the "1" and youare exactly correct.
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  4. #4
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    So, is the answer B = 2^(x)?
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  5. #5
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    No. It's 2^xn.
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  6. #6
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    Thank you very much. You are great!
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