The police discover a murder victim at 5:15 a.m. They measure the body
temperature of the victim and record it as 30°C. Hercule Marple arrives on the
scene of the crime 30 minutes later and measures the body temperature again.
He records it as 27°C.
The temperature of the room is recorded as 15°C and assumed to be constant.
Hercule Marple, knowing that normal body temperature is 37°C, wants to
estimate the time of death of the victim.
If the cooling process is modelled by the equation
q =q 0e^−kt , where q is the
excess
temperature (body temperature minus room temperature), and 0 q and
k
are constants, estimate the time of death.
(ii) When Miss Poirot arrives and investigates closely, she finds that the police and
Hercule have been sloppy recording the figures. The real measurements should
have been 29.6°C at 5:14am and 27.4°C at 5:46am, and the room temperature
was really 14.6°C. How far out is the original estimate of the time of death?