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Word Problem

  1. Mar 21, 2009 #1
    1. The problem statement, all variables and given/known data

    A yam is pust in an oven maintained at a constant temp of 250degrees C. Suppose that after 30 min the temp of the yam is 150degrees C and is increasing at a rate of 3degrees C/min. If the temp of the yam t minutes after it is put in the oven is modeled by
    T(t)=250-ae^(-bt), find a and b.

    2. Relevant equations



    3. The attempt at a solution

    I have no idea how to even start. Please help
     
  2. jcsd
  3. Mar 21, 2009 #2

    danago

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    Gold Member

    Just by looking at the question as stated, what are the values of:

    T(30)
    T'(30) ?

    How can you use these to find a and b?
     
  4. Mar 21, 2009 #3

    tiny-tim

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    Hi betsinda! :smile:

    Hint: what is Newton's law of cooling?
     
  5. Mar 22, 2009 #4
    I think I have found b

    180 = 250 - ae^-40b
    150 = 250 - ae^-30b


    -70 = -ae^-40b
    70/e^-40b = a

    -100 = -70/e^-40b * e^-30b
    100/70 = e^40b * e ^-30b
    10/7 = e^10b
    ln 10/7 = 10 b
    b = ln(10/7)/10

    but how do I find a?
     
  6. Mar 22, 2009 #5

    tiny-tim

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    a = 70e40b = 70(e10b)4 :wink:
     
  7. Mar 22, 2009 #6
    Thank you !
     
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