Question

A body was found at 6 a.m. in a warehouse where the temperature was 50°F. The medical examiner found the temperature of the body to be 66°F. What was the approximate time of death? Use Newton's law of cooling, with k = 0.1947.
T(t)=T[A] + (T[O]-T[A])e^-kt

Answer 1

Answer: 12 a.m.

Step-by-step explanation:

Answer 2

Using Newton's law of cooling, the approximate time of death was 12 a.m.

Newton's Law of Cooling

From the question, we are to determine the approximate time of death

From Newton's law of cooling formula, we have that

$T(t) = T_{s}+(T_{0}-T_{s})e^{-kt}$

Where t is time

$T(t)$ is the temperature of the body at time t

$T_{s}$ is the surrounding temperature

$T_{0}$ is the initial temperature of the body

and k is constant

From the given information,

T(t) = 66 °F

$T_{s}$ = 50 °F

k = 0.1947

Putting the parameters into the formula, we get

$66 = 50 + (98.6 - 50)e^{-0.1947t}$

NOTE: Initial temperature of the body will be the average temperature of a living human

∴ $T_{0}$ = 98.6 °F

$66 -50= 48.6e^{-0.1947t}$

$16= 48.6e^{-0.1947t}$

$\frac{16}{48.8} = e^{-0.1947t}$

$0.327869= e^{-0.1947t}$

$ln(0.327869)= -0.1947t$

-1.11514114 = -0.1947t

t = -1.11514114 / -0.1947

t = 5.727 hours

t ≅ 6 hours

This means at the time the body was found, the body had been dead for approximately 6 hours.

The body was found at 6 a.m.

The approximate time of death = 6 a.m. - 6 hours

The approximate time of death = 12 a.m.

Hence, the approximate time of death was 12 a.m.

Learn more on Newton's law of cooling here: https://brainly.com/question/13748261

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