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Math Help - Setting up and solving 2 nonlinear equations (Newton's Law of Cooling)

  1. #1
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    Setting up and solving 2 nonlinear equations (Newton's Law of Cooling)

    Original question:


    The instructor gave explicit step-by-step instructions on what she wanted.

    Step 1:


    My [correct] solution to step 1:


    Step 2:


    My [correct] solution to step 2:


    Step 3:


    My [correct] solution to step 3:


    Step 4 (this is where the problems begin):


    My solution to step 4 (now, this is a valid method to solve the problem BUT is NOT how she wants it to be solved!):


    Step 5


    My solution to step 5 (again, I get the CORRECT answer; but my process, according to my instructor is incorrect based on the given instructions):


    _______________

    If someone can please assist me in coming up with two nonlinear equations in the 2 variable t1 and K (step 4), I would forever appreciate you!

    Thank you very much.
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  2. #2
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    Re: Setting up and solving 2 nonlinear equations (Newton's Law of Cooling)

    Hey Dreamshot.

    For number 4, you should have something like this:

    (1) 34.5 = (37/2)*e^(-k(t+1)) + 16
    (2) 33.7 = (37/2)*e^(-kt) + 16

    Maple should solve these equations instead of the ones you gave.

    Can you explain how you got your equations for number 4?
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  3. #3
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Setting up and solving 2 nonlinear equations (Newton's Law of Cooling)

    T(t)=\text{T0}+c e^{-k t}

    solve to obtain:

    c=31.445
    k=0.044206

    then:

    T(death)=37 -> t_death=9.1327
    Last edited by MaxJasper; October 6th 2012 at 09:13 PM.
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