Coroners estimate time of death using the rule of thumb that a body cools about

Question

Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air temperature of 76 degrees F and a living body temperature of 98.6 degrees F, the temperature T(t) in degrees F of a body at a time t hours since death is given by T(t) = 76 + 22.6 e^(-kt).

a) For what value of k will the body cool by 2 degrees F in the first hour? k=

b) Using the value of k found above, after how many hours will the temperature of the body be decreasing at a rate of 1 degree F per hour?

c) Using the value of k found above, show by calculating both values that, 24 hours after death, the coroner's rule of thumb gives approximately the same temperature as the formula.

T(24)=

Rule of thumb gives: T=

Explanation / Answer

1. k=-In(32.6/34.6)=~ -0.06 2. In(0.5)/k=~0.753 3. T(24)=~72.29 coroner's rule 73.6

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