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.

T(t) =

(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.)

Thank you for the opportunity to help you with your question!

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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Jul 16th, 2015

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