Question

A body was found at midnight (12 a.m.) in a warehouse where the temperature was 55oF. The medical examiner found the temperature of the body to be 66oF. What was the approximate time of death? Use Newton's law of cooling, with k = 0.1947.

Answer 1

5 pm

Explanation:

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Answer 2

The solution would be like this for this specific problem:

T(t) = TA + (T₀ - TA) e^(-kt)

66 = 55 + (98.6 - 55) e^(-0.1947t)
11 = 43.6e^(-0.1947t)
11/43.6 = e^(-0.1947t)

ln(11/43.6) = -0.1947t

t = -ln(11/43.6) / 0.1947

t ≈ -ln(0.252294) / 0.1947
t ≈ -(-1.3771619) / 0.1947
t ≈ 1.3771619 / 0.1947
t ≈ 7.07325

So, the approximate time of death is 7 hours, 4 min, 23 seconds.