Exponential & Log Function Derivatives

Applications of Exponential & Log Function Derivatives

6. A casting is taken from one oven at 1500F and placed into another at 0F, but rising at a rate of 100o/hr. The temperature is then:

                T = 100t + 1500

Find the minimum temperature and when it occurs.

    You know the steps: Take the derivative with respect to time, zero it equal to zero, and solve.

        dT/dt = 100 + 1500(-0.2)e-0.2t

        0 = 100 – 300e-0.2t

        100 = 300e-0.2t

     1/3 = e-0.2t

        ln(1/3) = -.2t

        t = 5.49 hr

        The minimum temperature that corresponds to this is:

        T = 100(5.49) + 1500e-0.2(5.49) = 1049o

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