Note: You may want to consider the differential equation model for Newton's law of cooling to get started, and you will likely need to solve some algebraic equations numerically using technology.

A dead body was found outside at 11 PM. At that time, the temperature of the body was measured to be 83F. One hour later, the body's temperature was measured again and found to be 80F. Weather temperature data for that day indicate that the temperature had dropped steadily (i.e. linearly) from a high of 88F at 2 PM until midnight when it was 48F. Construct a model including all assumptions and definitions of all variables and use the model to determine the time of death to the nearest quarter hour. Show all work