Chapter 1, Problem 36P

Newton’s law of cooling gives the temperature T(t) of an object at time tin terms of T₀, its temperature at t = 0, and the temperature of the surroundings.

$T\left(t\right)=Ts+\left(T_0-T_s\right)\text{e}{-}^{kt}$

A police officer arrives at a crime scene in a hotel room at 9:18 PM. where he finds a dead body. He immediately measures the body’s temperature and finds it to be 79.5°F. Exactly one hour later he measures the temperature again and finds it to be 78.0°F. Determine the time of death, assuming that victim body temperature was normal (98.6°F) prior to death and that the room temperature was constant at 69°F.