This exercise uses Newton's Law of Cooling.

 Algebra Tutor: None Selected Time limit: 1 Day

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.
(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.)

hr

Jul 15th, 2015

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

Please let me know if you nea case for torture by michale levined any clarification. I'm always happy to answer your questions.
Jul 15th, 2015

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Jul 15th, 2015
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Jul 15th, 2015
Dec 5th, 2016
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