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Math Help - VERY hard differentiation analysis questions

  1. #1
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    VERY hard differentiation analysis questions

    Equation is:
    T represents temperature of water.
    T=Me-kt , where t is equal or greater than 0. t represents time.
    M= 55 and k = 0.0141 approx.

    Question:
    The time at which water is cooling at 1degree/second is -18.03, and hence is a puzzling answer( since time cannot take a negative value) . Explain why the answer is puzzling in terms of the student's model(equation)


    -----------------


    If 55loge (0.986) = -0.7754 approx.

    and T=55eloge (0.986t)

    Show algebraic steps to obtain approximation and state value of approximation to 2 decimal places
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  2. #2
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    Quote Originally Posted by delicate_tears View Post
    Equation is:
    T represents temperature of water.
    T=Me-kt , where t is equal or greater than 0. t represents time.
    M= 55 and k = 0.0141 approx.

    Question:
    The time at which water is cooling at 1degree/second is -18.03, and hence is a puzzling answer( since time cannot take a negative value) . Explain why the answer is puzzling in terms of the student's model(equation)


    -----------------


    If 55loge (0.986) = -0.7754 approx.

    and T=55eloge (0.986t)

    Show algebraic steps to obtain approximation and state value of approximation to 2 decimal places
    I suppose you mean T = Me^{-kt} ???

    T' = -kMe^{-kt}

    at t = 0, T' = -kM = -.7755 \, \frac{deg}{sec}

    since T'' = k^2Me^{-kt} > 0 for all t \ge 0 , the value of T' will increase over time.
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  3. #3
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    Quote Originally Posted by delicate_tears View Post
    Equation is:
    T represents temperature of water.
    T=Me-kt , where t is equal or greater than 0. t represents time.
    M= 55 and k = 0.0141 approx.

    Question:
    The time at which water is cooling at 1degree/second is -18.03, and hence is a puzzling answer( since time cannot take a negative value) .

    Why can't t take a negative value? t= 0 must refer to some specific point in time. t negative refers to time before that.

    Explain why the answer is puzzling in terms of the student's model(equation)


    -----------------
    If 55loge (0.986) = -0.7754 approx.

    and T=55eloge (0.986t)

    Show algebraic steps to obtain approximation and state value of approximation to 2 decimal places
    Follow Math Help Forum on Facebook and Google+

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