Question

question 3 of 10
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 newtons law of cooling, with ( k = )
0.1947.

t(t)=t_{a}+left(t_{0}-t_{a}
ight) e^{-k t}

a. midnight (12 a.m.)
b. 5 a.m.
c. 3 a.m.
d. 2 a.m.

Explanation:

Step1: Define known values

$T_A=50^\circ\text{F}, T(t)=66^\circ\text{F}, T_0=98.6^\circ\text{F}, k=0.1947$

Step2: Substitute into cooling formula

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

Step3: Simplify the equation

$16 = 48.6e^{-0.1947t} \implies \frac{16}{48.6} = e^{-0.1947t} \implies 0.3292 = e^{-0.1947t}$

Step4: Take natural logarithm

$\ln(0.3292) = -0.1947t \implies -1.110 = -0.1947t$

Step5: Solve for t

$t = \frac{1.110}{0.1947} \approx 5.7$ hours

Step6: Find death time

6 a.m. - 6 hours ≈ midnight

Answer:

A. Midnight (12 a.m.)