Description
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 65°F.
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.)
hr
Explanation & Answer
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T(t) = Ta + (To - Ta)e^-kt.....where Ta is the ambient temperature, To is the initial temperature and t is time.
then, T(t) = 55 + (98.6 - 55)e^-0.1947t
=> T(t) = 55 + 43.6e^-0.1947t
so, 73 = 55 + 43.6e^-0.1947t
=> e^-0.1947t = 18/43.6
=> -0.1947t = ln(18/43.6)
so, t = -[ln(18/43.6)]/0.1947 => 4.54 hours