Answer:
5 p.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,
T(t) = 66 F,
[tex]t_a[/tex] = 55 F,
Putting the values,
[tex]\Rightarrow 66=55+(98.6-55)e^{-0.1947\cdot t}\\\\\Rightarrow 66=55+(43.6)e^{-0.1947\cdot t}\\\Rightarrow (43.6)e^{-0.1947\cdot t}=11\\\Rightarrow e^{-0.1947\cdot t}=\dfrac{11}{43.6}=0.2523\Rightarrow \ln e^{-0.1947\cdot t}=\ln 0.2523\\\Rightarrow -0.1947\cdot t\times \ln e=\ln 0.2523\\\Rightarrow -0.1947\cdot t\times 1=\ln 0.2523\\\Rightarrow t=\dfrac{\ln 0.2523}{-0.1947}\\\Rightarrow t=7\ h[/tex]
Therefore, the time of death was 7 hours before midnight i.e at 5 pm.
