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  1. #1

    [Math] Confusing Word Question

    Hey everyone, I had this EC problem on my last test (which I horridly failed) and I was just curious on how it would be solved.

    A Petri dish hosts a healthy colony of bacteria. Once a minute every bacterium divides into two. The colony was founded by a single cell at noon. At exactly 12:43 (43 minutes later) the Petri dish was half full. At what time will the dish be full?

  2. #2
    Um ... the dish is exactly half full, and the bacteria double every minute .. so in 1 minute's time, half-full becomes full. So .. 12:44

  3. #3
    One minute later.

  4. #4
    Well if it is half full at 12:43 and every bacteria divides into 2 new ones every minute, logically it would be full at 12:44 would it not? An exponential problem I believe.

  5. #5
    Titan Reeve's Avatar
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    Quote Originally Posted by Litesung View Post
    Hey everyone, I had this EC problem on my last test (which I horridly failed) and I was just curious on how it would be solved.
    I'd think if the colony doubles in population every minute, the answer would be 2^43, or 8,796,093,022,208.

    Edit. I suck at reading comprehension. Yes, the dish would be full at 12:44.
    Go and tell my baby sister
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  6. #6
    at 12:44

    your teacher successfully trolled you
    Pokemon X Friendcode : 5257-9535-0556 - Poison Safari, Drapion - Kakuna - Ariados
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  7. #7
    At 43 minutes you would have 8,976,093,022,208 bacterium and that is half full. Thus doubling that number would make it full. It would double in the next minute cycle so you would be full at 44 minutes later, or 12:44.

  8. #8
    Quote Originally Posted by Reeve View Post
    I'd think if the colony doubles in population every minute, the answer would be 2^43, or 8,796,093,022,208.

    Edit. I suck at reading comprehension. Yes, the dish would be full at 12:44.
    Edit: My reading comprehension is horrible too

  9. #9
    It does look like your prof. was running a derp check - in 1 minute it will double its size, so if the container is half full - 1 minute later it will double and be full.

  10. #10
    op, you goofball, read the question again lol :3

  11. #11
    If it's half full, and every minute the bacteria divides in two, that means it'll be...

    (1/2) + (.5/.5) or
    (1/2) + (1/4)
    (2/4) + (1/4) = 3/4 full at 12:44

  12. #12
    Titan Reeve's Avatar
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    Quote Originally Posted by Litesung View Post
    If it's half full, and every minute the bacteria divides in two, that means it'll be...

    (1/2) + (.5/.5) or
    (1/2) + (1/4)
    (2/4) + (1/4) = 3/4 full at 12:44
    No. You're dividing the dish. You should be multiplying the bacteria. Each minute, the population of the bacteria doubles since each bacteria divides into 2 bacteria. The dish will be full at 12:44.
    Go and tell my baby sister
    Not to do what I have done
    Go and spurn that house down in New Orleans
    They call the Rising Sun

  13. #13
    Okay so basically, if the whole dish divides into two...

    (1/2)/(1/2) = (1/2)*2 = 1

    Okay that makes sense. I was thinking at the time "Wait.. the whole divides into a half?"

  14. #14
    Herald of the Titans Lenonis's Avatar
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    Interesting -- that's less a math question and more a logic question. The only relevant parts of the question are that the bacteria split into 2 every minute and the dish is 1/2 full at 12:43. The rest is there to confuse you...you don't really need math to solve it.

    Definitely a tricky question if you don't realize it's a trick.

  15. #15
    Good to know, thanks. My teacher likes to put the most difficult scenarios for each type of question, and it seems like there's always a 'trick' to each one.

  16. #16
    Scarab Lord Trollskalden's Avatar
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    Quote Originally Posted by Litesung View Post
    Good to know, thanks. My teacher likes to put the most difficult scenarios for each type of question, and it seems like there's always a 'trick' to each one.
    Same here. Half his tests contains silly trick questions, like what is (cosx+sinx)^2012

  17. #17
    Quote Originally Posted by Tomatketchup View Post
    Same here. Half his tests contains silly trick questions, like what is (cosx+sinx)^2012
    You would have to provide an x for that one, mate . If you want a numerical answer, that is. Or you can say exp(2012*i*x)
    Last edited by guff; 2012-11-27 at 08:11 PM.

  18. #18
    Scarab Lord Trollskalden's Avatar
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    Quote Originally Posted by guff View Post
    You would have to provide an x for that one, mate . If you want a numerical answer, that is. Or you can say exp(2012*i*x)
    My bad, I meant that cos^2x + sin^2x = 1.

  19. #19
    Fluffy Kitten conscript's Avatar
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    That is a horrible question. On one hand it implies it would be full in one minute. But that is only if you assume that the cells divide and grow to full size that rapidly. There is no indication in the question at all that the cells divide and then grow back to the original size rather than simply divide. So not knowing the growth rate of the bacterium, you either decide that it takes literally one minute for them to double in size and divide (making the answer 1 minute) or since no indication of growth is given, the answer is never.

  20. #20
    Herald of the Titans Lenonis's Avatar
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    Quote Originally Posted by conscript View Post
    That is a horrible question. On one hand it implies it would be full in one minute. But that is only if you assume that the cells divide and grow to full size that rapidly. There is no indication in the question at all that the cells divide and then grow back to the original size rather than simply divide. So not knowing the growth rate of the bacterium, you either decide that it takes literally one minute for them to double in size and divide (making the answer 1 minute) or since no indication of growth is given, the answer is never.
    Oh geez. You are like me. You overthink the question and end up totally confused about the right answer.

    I'm studying for a certification exam and I get into the bad habit of overthinking the question to the point where none of the answers make sense.

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