36 Police discover the body of a murder victim at 1000pm At

36) Police discover the body of a murder victim at 10:00pm. At that time, the temperature of the body is 87°F·One hour later, the temperature is 86\"F . If the temperature of the roomis 70°F, and we assume that when the murder occurred, the person had a normal body temperature of 98.6 F estimate the time of death

Solution

applying newtons law of cooling formula

T(t) = Ta + (To - Ta ) e^-kt

T(t) = temperature of body at time t

Ta = temperature of surrounding

To = initial temperature

86 = 70 + ( 87 - 70 ) e^-k

86 - 70 = 17e^-k

k = .0606

now plugging initial temperature as 98.6 and final as 87

87 = 70 + ( 98.6 - 70 ) e^-.0606t

87- 70 / 28.6 = e^-.0606t

t = 8.58

so, murder happend around 8.58 hours before 10.pm

= around 1:30 pm