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

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

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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