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Law of cooling and Exponential growth

  1. Oct 9, 2007 #1
    1. The problem statement, all variables and given/known data
    A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the temperature is 75 degrees F. When will the turkey have cooled to 100 degrees F?


    2. Relevant equations
    dT/dt=k(T-Ts) where Ts=temperature of the surrounding
    y(t)=y(0)e^kt



    3. The attempt at a solution
    I solved T(t)=75+110e^(ln .682)t/30

    Solving for t:
    100=75+110e^(ln .682)t/30
    t=10

    I know that t=10 isn't right, but I don't know what I did wrong. Any takers?
     
  2. jcsd
  3. Oct 9, 2007 #2
    How did you solve for k?

    Just quickly I got:

    [tex]\frac{1}{k}ln(\frac{25}{110})[/tex]
     
  4. Oct 9, 2007 #3
    To solve for k I used the fact that y(30)=150-75=75
    So, 110e^30k=75
    e^30k=.682
    30k=ln .682
    k= ln .682/30
     
  5. Oct 10, 2007 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    And how did you know that y(30)= 75? You didn't tell us anything about the temperature of the turkey 30 minutes after being take out of the oven!
     
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