A dead body is discovered at noon on Friday where the air te

Solution

let the temperature of the body at any time be T(t) By newton\'s law of cooling dT/dt = -k(T-To) where T is the instantaneous temperature and To is the temperature of surroundings given as 70 degF integrating you will get ln(T-70) = -kt + C when t = 0, T = 76 so, C = ln6 hence, ln(T-70) = -kt + ln6 or, ln((T-70)/6) = -kt or, T(t) = 70 + 6exp(-kt) when t = 1 hour, T = 75.3 degF we will get 75.3 = 70 + 6exp(-k) exp(-k) = 5.3/6 k = 0.1241 (hr)^-1 so the equation of temperature is T(t) = 70 + exp(-0.1241t) ................(t in hours, T in degF)