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Bacteria growth can be modelled by the function N(t)=No[3^(t/35)]

  1. Jun 7, 2012 #1
    1. The problem statement, all variables and given/known data
    The bacteria in a tuna sandiwch left out of refrigerator grows exponentially. The number of bacteria in a sandwich at any time, t, in minutes can be modelled by the function N(t)= No[3^(t/35)]
    a)if there are 600 bacteria initially, how long will it take for the bacteria population to grow to 1800
    b) at what rate is the bacteria population growing after 15 minutes

    2. Relevant equations
    N(t)= No[3^(t/35)]


    3. The attempt at a solution
    a)I figured out part a, t=35
    1800=600[3^(t/35)]
    ln3=(t/35)ln3
    t=35 minutes

    b) N(t)= N(t)= No[3^(t/35)]
    N'(t)=(t/35)(600)(3)
    I'm not sure where to go from there..
     
  2. jcsd
  3. Jun 7, 2012 #2
    You should check your derivative, N'(t). Remember that this is an exponential; the derivative of an exponential is still an exponential; t should never come out of the exponential.

    Once you've done that, though, really all you need to do is plug in t=15 to N'(t).
     
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