At 9:00 PM a coroner arrived at a hotel room of a murder victim. The temperature of the room was 70 Degrees F. It was assumed that the victim had a body temperature of 98.6 degrees F (AT THE TIME OF DEATH)(not at 9:00 PM). The coroner took the victim's temperature at 9:15 PM at which it was 83.6 degrees F and again at 10:00 PM at which it was 80.3 degrees F.
At what time did the victim die?
This problem is supposed to be solved by usinf Newton's Law of Cooling :
T(t) = T_s + (T_0 - T_s)e^(Kt).
Please see the attached file.
Newton's Law of Cooling describes the cooling of a warmer object to the cooler temperature of the environment. Specifically we write this law as,
T (t) = Te + (T0 − Te ) e - kt, ...
The solution explains in details Newton's Law of Cooling and then provide step-by-step analysis for the problem.