This exercise uses Newtons Law of Cooling Newtons Law of Coo

This exercise uses Newton\'s Law of Cooling. Newton\'s Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6 degree F. Immediately following death, the body begins the cool. It has been determined experimentally that the of constant in Newton\'s Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the is 70 degree F. (a) Find a function T(t) that models the temperature t hours after death. T(t) = (b) If the temperature of the body is now 79 degree F, how long ago was the time of death? (Round your answer to the nearest whole number.)

Solution

formula for newton\'s law of cooling is T(t)=T_s +e^-kt(T_o-T_s)

where  T(t) is temperator of the body after time t , k is constant ,T_s =surrounding temperature , T_o =initial temperature of the body

(a)

T(t)=70+e^-0.1947t(98.6-70)

=>T(t)=70+ 28.6e^-0.1947t

(b)

given T(t)=79

=>79=70+ 28.6e^-0.1947t

=>28.6e^-0.1947t=9

=>e^0.1947t=28.6_/9

=>0.1947t=ln(28.6_/9)

=>t=(1_/0.1947)ln(28.6_/9)

=>t6

so, the death occured 6 hours ago