Math Problem Statement

A dead body was found within a closed room of a house where the temperature was a constant 70° F. At the time of discovery the core temperature of the body was determined to be 85° F. One hour later a second measurement showed that the core temperature of the body was 80° F. Assume that the time of death corresponds to t_0 and that the core temperature at that time was 98.6° F. Determine how many hours elapsed before the body was found.

Solution

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Math Problem Analysis

Mathematical Concepts

Differential Equations
Exponential Decay
Newton's Law of Cooling

Formulas

dT/dt = -k(T(t) - T_a)
T(t) = T_a + (T_0 - T_a)e^{-kt}

Theorems

Newton's Law of Cooling

Suitable Grade Level

Undergraduate level (Calculus and Differential Equations)