Newton's emperical law of cooling/warming of an object is given by the linear firstorder differential equations; (*)where k is a constant of proportionality, t is time, t (t) is the temperature for theobject for t > 0 and tambient is the ambient temperature, that is, the temperature ofthe medium around the object. in general, tambient is assumed to be constant. problem: in fixing time of death, coroners use a formulation based on newton's lawof cooling (*). this law states that the rate of change in the temperature t (t) of abody in this case is directly proportional to the difference between the temperature of the body and the ambient temperature surrounding the body. suppose that a coroner arrives at 11: 00 am to investigate a murder. he finds that the body is submerged in a pool of water. upon arrival he takes the temperature of the water and finds it is 76.10 f (degrees fahrenheit). since the water is in a protected environmentit is reasonable that the temperature for the surroundings may be presumed to haveremained constant. when the coroner arrived he also took the temperature of thebody and recorded it as 94.55 f . one hour later the temperature of the body is taken1again and recorded as 93.2 f before it is removed from the water. assumingthe body's temperature was a normal of 98.6 f at the time of death, at what timedoes the cooling law (*) predicts that the murder took place? hint: first, solve fort (t) in the differential equation (*) :