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Exponential and Logarithmic Functions

  1. Apr 22, 2012 #1
    Can anyone check my work? I'm doubtful of my answer.

    1. The problem statement, all variables and given/known data

    The bacteria in a 4-liter container double every minute. After 60 minutes the container is full. How long did it take to fill half the container?

    2. Relevant equations

    I used:

    F = A × 260
    (1/2)F = A × 2x

    F is "full", A is the starting amount of bacteria, and x is time in minutes.

    3. The attempt at a solution

    (1/2)(A × 260) = A × 2x

    (1/2)(260) = 2x
    260-1 = 2x
    60 -1 = x
    59 minutes = x
     
  2. jcsd
  3. Apr 23, 2012 #2
    Well done!

    Now that you know the answer, you can understand that you could have got the answer by inspection. If the bacteria doubles every minute, then the container MUST HAVE BEEN half full after 59 minutes. IF ANF ONLY IF THIS HAPPENS can you double the bacteria and get the full container after the next minute (i.e. after 60 minutes).
     
  4. Apr 23, 2012 #3
    Thanks!

    Oh, wow. I never though of it that way! That would have saved a lot of work, haha.
     
  5. Apr 23, 2012 #4
    Thanks!

    Oh, wow. I never though of it that way! That would have saved a lot of work, haha.
     
  6. Apr 23, 2012 #5

    Curious3141

    User Avatar
    Homework Helper

    This is one of those well known trick questions. Sometimes appears on informal "for fun" IQ tests. :biggrin:
     
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