Mathematics: A body was found at midnight in a warehouse where the temperature was 55. The medical examiner found the temperature of the body to be 66. What was the approximate time of death?

its cStep-by-step explanation:...

A body was found at midnight in a warehouse where

Ответ:

jesh0975556

28.01.2022

Mathematics

5 p.m.

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,

$\Rightarrow 66=55+(98.6-55)e^{-0.1947\cdot t}\\\\\Rightarrow 66=55+(43.6)e^{-0.1947\cdot t}\\\Rightarrow (43.6)e^{-0.1947\cdot t}=11\\\Rightarrow e^{-0.1947\cdot t}=\dfrac{11}{43.6}=0.2523\Rightarrow \ln e^{-0.1947\cdot t}=\ln 0.2523\\\Rightarrow -0.1947\cdot t\times \ln e=\ln 0.2523\\\Rightarrow -0.1947\cdot t\times 1=\ln 0.2523\\\Rightarrow t=\dfrac{\ln 0.2523}{-0.1947}\\\Rightarrow t=7\ h$

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

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A body was found at midnight in a warehouse where the temperature was 55. The medical examiner found the temperature of the body to be 66. What was the approximate time of death?

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