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A body of an unknown temperature was placed in a room that was held at 30°F. After 10 minutes, the body's temperature was 0°F, and 20 minutes after the body was placed in the room the body's temperature was 15°F. Estimate the body's initial temperature.

Thank you!!

  • Calc -

    I am going to assume that the heat flow into the body is proportional to the difference between body temp T and 30 and rate of change of T is proportional to heat flow .

    dT/dt = k (30-T)

    try T = -ae^-kt + 30
    that is 30 at t-->oo and 30-a at t = 0
    0 = -a e^-10k + 30
    15= -a e^-20k + 30

    30 = a e^-10k
    45 = a e^-20 k

    a = 30/e^-10k

    45 = 30 (e^-20k/e^-10k)

    45/30 = e^-10k

    I think you can take it from there, check arithmetic

  • Calc -

    the 8th line is the simplification of the sixth line,,, im wandering why it is 45? is the algebraic solution wrong?

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