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    I was doing a past paper on OCR biology and I came across this question:

    "A single bacterium will divide many times to form a colony. Bacteria are added to a Petri dish. After 24 hours there are several colonies of bacteria.

    The smallest number of bacteria that could have been present at the start of the 24 hour period is 8.

    A single bacterium can divide 20 minutes.

    One of the colonies has 4096 bacteria.

    Calculate how long this colony has been growing. Show working."


    I've looked at the mark scheme and the answer is 240 minutes or 4 hours but I don't understand how they got this answer? can someone please explain this to me?
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    Assuming the colony starts at 8 and doubles every twenty minutes:

    The number of bacteria in the colony is 8 * 2 ^ n, where n is the number of time periods passed (each time period is 20 minutes). At one point, the number in the colony is 4096, so we have 8 * 2 ^ n = 4096

    This simplifies to 2 ^ n = 512. Then, using a calculator, type log (base 2) [512], and you should get n = 9. Thus the time taken is 9 * 20 = 180 minutes or three hours.

    Either the mark scheme is wrong or you've misread the question. If the colony size started at 1 then n would be 12 and thus time taken would be 240 minutes.
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    You just half the number of bacteria (4096) until you reach 1. You then times the number of halves by 20 (12 x 20) and then you get 240 minutes as an answer.
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    or just 20 x (log2(4096)) to get 240, but hey, either works.
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    As its biology I suspect that they want you to keep doubling 8 until you get 4096.
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    (Original post by TimGB)
    Assuming the colony starts at 8 and doubles every twenty minutes:

    The number of bacteria in the colony is 8 * 2 ^ n, where n is the number of time periods passed (each time period is 20 minutes). At one point, the number in the colony is 4096, so we have 8 * 2 ^ n = 4096

    This simplifies to 2 ^ n = 512. Then, using a calculator, type log (base 2) [512], and you should get n = 9. Thus the time taken is 9 * 20 = 180 minutes or three hours.

    Either the mark scheme is wrong or you've misread the question. If the colony size started at 1 then n would be 12 and thus time taken would be 240 minutes.
    (Original post by thomas-cowley)
    You just half the number of bacteria (4096) until you reach 1. You then times the number of halves by 20 (12 x 20) and then you get 240 minutes as an answer.
    (Original post by thomas-cowley)
    or just 20 x (log2(4096)) to get 240, but hey, either works.
    (Original post by B_9710)
    As its biology I suspect that they want you to keep doubling 8 until you get 4096.
    Thanks everyone!!
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    (Original post by Maz0110)
    Thanks everyone!!
    No problem; I love the maths questions haha!
 
 
 
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