2. According to Newton’s Law of Cooling, the rate of change ofthe temperature of an object can be modeled using the followingdifferential equation:
dT/dt = k(T-TR)
where T is the temperature of the object (in ◦F), TR is the roomtemperature (in ◦F), and κ is the constant ofproportionality.
On a crime show, the detective discovers a dead body in a hotelroom.
(a) Write the differential equation to describe the change intemperature of the body if κ = −0.405 and thermostat in the hotelroom is set at 70◦F.
(b) Solve the differential equation using an appropriate method.State the method you used and show your work.
(c) Assuming the victim was a healthy 98.6â—¦F at the time of themurder, we have the initial condition that T(0) = 98.6. Find theparticular solution to the IVP.
(d) If the body temperature is 85â—¦F when the crime scene isdiscovered, how long has the victim been dead? (Assume t ismeasured in hours.)
