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  3. 2. according to newton’s law of cooling, th

2. According to Newton’s Law of Cooling, the rate of change of the temperature of an...

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Advance Math

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.)

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