It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 65°F.
(a) Find a function T(t) that models the temperature t hours after death.
(b) If the temperature of the body is now 71°F, how long ago was the time of death? (Round your answer to the nearest whole number.)
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According to Newton's Law of cooling
T(t) = Tamb +(To - Tamb)*e(-kt)
where To = initial temperature at t = 0 ; Tamb = ambient temp
(a) T(t) = 65+ (98.6-65)*e^(-0.1947t) solving we get T(t) = 65 + 33.6 * e^(-0.1947t) Answer
(b) 71 = 65+33.6 * e^(-0.1947t)
e^(-0.1947t) = 0.178 ; or we can write -0.1947 t = -1.7237
or we get t = 8.84 hours t = 9 hours (Answer)
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