Question

Question 1. (4 marks) Estimating the time of a victim’s death during homicide investigations is a complex problem that cannot be solved by analysising simple equations or functions of one variable. However, many mathematical texts examine time of death estimation based around analysis of Newton’s Law of Cooling. Such analysis is based on implicit simplifying assumptions that: the only dependent variable of interest in determining the time of death is the victim’s body temperature, T(t); the victim’s baseline body temperature when alive, T0, is known; and the air temperature of the victim’s surroundings, Ts, is constant. Here we will examine such a problem.
(a) Assume that immediately following death, a victim’s body begins to cool from a standard healthy body temperature of 37◦ Celsius. Further, assume that experimental work has determined that the rate constant in Newton’s Law of Cooling for a human body is approximately k = 0.1947 when time t is measured in hours. Determine a function derived from Newton’s Law of Cooling, T(t), that models the temperature of a victim’s body t hours after death, assuming that the temperature of the body’s surroundings is a constant 18◦ Celsius

. (b) If the temperature of the victim’s body is now 25◦, how long ago was their time of death?

(c) If the victim’s body temperature at death had instead been 36.3◦ Celsius (within the range of normal body temperatures for a healthy adult), what time of death would be estimated via a Newton’s Law of Cooling model? By what duration does this estimate differ to the time that you determined in part (b)?

(d) In reality, how might the modelling assumptions made to address this problem be violated?

Question 2. (3 marks)A hair sample from a Coptic mummy was found to contain 61% of the relative proportion of carbon-14 found in living matter and the atmosphere. Approximately how long before the carbon-14 measurements were made had the mummy been buried? (The half-life of carbon-14 is 5730 years.)

Question 3. (3 marks) The most desctructive earthquake in contemporary Australian history occurred in Newcastle, NSW, in 1989. The earthquake had a magnitude of 5.6.
(a) Assuming seismograph readings were taken 100km from the epicentre of the earthquake, what was the corresponding intensity of the earthquake (measured by the amplitude of a seismograph reading in centimetres)?

Answer 1

b5 5干30 t- 5730x In Co.'I) eans

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