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A body was found at midnight (12am) in a warehouse where the temperature was 55 degrees Fahrenheit. The medical examiner found the temperature of the body to be 66 degrees Fahrenheit. What was the approximate time of death? Use newtons law of cooling with k=0.1947. T(t)=t (base a)+(t (base o)-t(base))e^(-kt)

A4 pm
B6 pm
C5 pm
D3 pm

Verified Answer :

narusasu

i believe it is c. 5pm

InesWalston

Answer:

C. 5 pm

Step-by-step explanation:

Newton's law of cooling-

\(T(t)=t_a+(t_0-t_a)e^{-kt}\)

where,

\(t_0\) = the initial temp. = 98.6 F (human body temp.)

k = 0.1947,

\(T(t)\) = 66 F,

\(t_a\) = 55 F,

Putting the values,

\(\Rightarrow 66=55+(98.6-55)e^{-0.1947\cdot t}\)

\(\Rightarrow 66=55+(43.6)e^{-0.1947\cdot t}\)

\(\Rightarrow (43.6)e^{-0.1947\cdot t}=11\)

\(\Rightarrow e^{-0.1947\cdot t}=\dfrac{11}{43.6}=0.2523\)

\(\Rightarrow \ln e^{-0.1947\cdot t}=\ln 0.2523\)

\(\Rightarrow -0.1947\cdot t\times \ln e=\ln 0.2523\)

\(\Rightarrow -0.1947\cdot t\times 1=\ln 0.2523\)

\(\Rightarrow t=\dfrac{\ln 0.2523}{-0.1947}\)

\(\Rightarrow t=7\ hr\)

Therefore, the time of death was 7 hours before 12 am i.e at 5 pm.


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