Question

Time of death determinations can be made using Newton's Law of Heating (or cool- ing, depending on which way the temperature is going), which predicts that the rate of change of temperature is proportional to the difference between the temperature of the object and the ambient temperature of the environment. (a) Last time, you assumed that the death occurred in a place where the temperature was constant. Now, an exercise in adjusting your differential equation! Write a new differ- ential equation that models the scenario where the ambient temperature in the room smoothly fluctuates between 70 degrees at midnight and 90 degrees at noon everyday Use hours as the units on the independent variable. (b) Plot the slope field and point out the transient (short-term) and the steady-state (long- term) portions of the solution for a variety of initial conditions. Use a window setting that shows a few days worth of temperature fluctuations. (c) What happens to the temperature of the body in the long run? How does this affect the forensic investigators working on a case?

Answer 1

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