**Project 2 – The Murder Mystery**

*Purpose**: To use Newton’s Law of Cooling to determine the time of a murder.*

*Newton’s Law of Cooling states that if a body with initial temperature T**i **is placed in surroundings with temperature T**s **, the body will either cool or warm to temperature T(t) after time t, in minutes, according to the equation:*

*T(t) = T**s **+ (T**i **– T**s**)e**-kt **,where k represents the cooling constant for the body*

The police discover the body of a murder victim inside a small convenience store. Critical to solving the crime is determining when the murder was committed. The coroner arrives at the murder scene at 9:00 PM. She immediately takes the temperature of the body and finds it to be 84.6ï‚°F. She then takes the temperature 1 hour later and finds it to be 83.4ï‚°F. The temperature of the room is 70.0ï‚°F. The temperature of a nearby room which is a walk-in cooler is 40ï‚°F.(Assume the body’s temperature is 98.6ï‚°F at the time of the murder).

1)One theory of the crime is that the body remained in the room the entire time between the murder and the coroner’s arrival. Determine when the murder committed according to this theory. (*Round your answer to the nearest 1⁄2 hour*)

2) A second theory of the crime is that the body may have been located in the walk-in cooler and moved to the room where it was found just minutes before the coroner arrived.Determine when the murder committed according to this 2nd theory. (*Round your answer to the nearest 1⁄2 hour*)

3) A third theory of the crime is that the body may have been located in the walk-in cooler for 1 hour and then moved to the room where it was found. Determine when the murder committed according to this 3rd theory. (*Round your answer to the nearest 1⁄2 hour*)

4) If fighting was heard by the tenant in the apartment above the convenience store at 4:40 pm, which theory is most likely correct? Explain your answer.

*Be sure to show all of your work neatly and clearly. For each equation that you use, create a list of the data used, explain what each equation represents and what the “unknown” in the equation represents. Show all the steps used in solving each equation.*

*note**: must show all the work! *

**clear simple explanations no complex words.**.

Subject | Mathematics |

Due By (Pacific Time) | 05/07/2014 08:00 am |

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