SOLUTION: This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Im

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Question 1119971: This exercise uses Newton's Law of Cooling.
Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. 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 55°F.
(a) Find a function T(t) that models the temperature t hours after death.
b) If the temperature of the body is now 79°F, how long ago was the time of death? (Round your answer to the nearest whole number.)
Answer by solver91311(24713) About Me  (Show Source):
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The rate of change of temperature of the body at time is . By Newton's Law of Cooling, this rate of change is proportional to the instantaneous difference between the current temperature of the body and the constant ambient temperature. Hence:



Let where is ambient.

Then



because is a constant.

Hence



But this function is well-known to be:



Since we are given for time in hours, we can write:



If , solve



for hours.


John

My calculator said it, I believe it, that settles it