math problem question

Question

At 11:00 am, a body was found within a closed room of a mansion where the air temperature is a constant 70 degrees F. At the time of discovery, the core temperature was determined to be 85 degree F. One hour later, a second measurement showed the core temperature of the body was 80 degrees F. Assume the core temperature of the body at the time of death was 98.6 degrees F. Use Newton’s Law of Cooling to determine the time of death. Hint: Let t=0 represent 11:00 am and work backwards to 98.6 degrees F.

 

Answer 1

Actually Newton's Law of Cooling is that the rate of temperature change of a body is directly proportional to the difference between the body and its environment.

That is a differential equation which has general solution in this problem of

T(t) = 70 + Ce^kt

T(0) = 85 gives you C and T(1) = 80 gives you k.

The answer will be the value of t (which you will find to be negative) which makes T(t)=98.6, that is,

98.6 = 70 + Ce^kt, solved for t.