Coroners use a formulation based on newton's cooling legislation to fix the time of death. in this case, the rate of change in a body's t (t) temperature is directly proportional to the difference between the body's temperature and the surrounding body's ambient temperature. suppose a coroner comes to investigate a murder at 11: 00 am. he discovers the body plunging into a pool of water. upon arrival he takes the water temperature and discovers it to be 76.10 (degrees fahrenheit). since the water is in a safe setting, it is sensible to presume that the temperature remained constant for the surroundings. he also took the body temperature when the coroner came and reported it as 94.55 degrees fahrenheit.
one hour later the body’s temperature is recovered and registered as 93.2 degrees fahrenheit before removing it from the water. assuming the temperature of the body was a standard 98.6 degrees fahrenheit at the moment of death, at what time des the cooling law predict the killing occurred?
this implies the time of death before 11: 00 is 0.1985 hours. 0.1985* 60 minutes= 11.91 minutes, 11 minutes, 91% of a minute. seconds 0.91* 60= 54.6 seconds.
the time of death is therefore 11 minutes and 54.6 seconds before 11: 00. death time occurred at about 10: 48 and 5.4 seconds.
can you plot the temperature as a function of time using desmos. com? show all steps.