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 50°F.
(a) Find a function T(t) that models the temperature t hours after death.
(b) If the temperature of the body is now 73°F, how long ago was the time of death? (Round your answer to the nearest whole number.)
- Wayne DeguManLv 72 months ago
T(t) = Ta + (To - Ta)e^(-kt)
so, T(t) = 50 + 48.6e^-0.1947t
Then, when T(t) = 73 we would have:
50 + 48.6e^-0.1947t = 73
Can you take it from there?
- rotchmLv 72 months ago
Hint: State Newton's Law of Cooling explicitly, or via a DE. This, you should know by heart. Once you give the formula you were supposed to learn, we will then show you how to use it.
Hopefully no one will spoil you the answer. That would be very irresponsible of them.