Answer:
Midnight (12 a.m.)
Step-by-step explanation:
Newton's law of cooling-
[tex]T(t)=t_a+(t_0-t_a)e^{-kt}[/tex]
where,
[tex]t_0[/tex] = the initial temp. = 98.6 F (human body temp.)
k = 0.1947,
[tex]T(t) = 66[/tex] F,
[tex]t_a = 55[/tex] F,
[tex]\Rightarrow 66=50+(98.6-50)e^{-0.1947\cdot t}[/tex]
[tex]\Rightarrow 66=50+(48.6)e^{-0.1947\cdot t}[/tex]
[tex]\Rightarrow (48.6)e^{-0.1947\cdot t}=16[/tex]
[tex]\Rightarrow e^{-0.1947\cdot t}=\dfrac{16}{48.6}[/tex]
[tex]\Rightarrow \ln e^{-0.1947\cdot t}=\ln \dfrac{16}{48.6}[/tex]
[tex]\Rightarrow -0.1947\cdot t=\ln \dfrac{16}{48.6}[/tex]
[tex]\Rightarrow t=\dfrac{\ln \frac{16}{48.6}}{-0.1947}=5.7\approx 6[/tex] hr
Therefore, the time of death was 6 hours before 6 am i.e at midnight (12 a.m.)
