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Calculus word problem

  1. Oct 21, 2015 #1
    A bacteria culture initially contains 2000 bacteria and doubles every half hour. The formula for the population is p(t)=2000 e^{kt} for some constant k. (You will need to find k to answer the following.)

    Find the size of the baterial population after 40 minutes.

    Find the size of the baterial population after 10 hours.

    Soltn:
    When t = 0.5 hour, p(t) = 4000, so we have

    4000 = 2000e^(0.5k)

    2 = e^(0.5k)

    ln(2) = 0.5k

    k = ln(2)/0.5 = 1.386294361

    Where did 4000 part come from?

    Thank you
    Where
     
  2. jcsd
  3. Oct 21, 2015 #2

    SteamKing

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    A bacteria culture initially contains 2000 bacteria and doubles every half hour.
     
  4. Oct 21, 2015 #3
    @SteamKing but it's 40 minutes so shouldn't it be a little more than that?
     
  5. Oct 21, 2015 #4

    Ray Vickson

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    No. You are still just working out the value of k. You have not gotten to the 40 minute problem yet.
     
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