A body was found in a room when the room’s temperature was 70F. Let f (t) denote the temperature of the body t hours from the time of death. According to Newton’s law of cooling, f satisfies a differential equation of the form y′ = k(T - y).

(a) Find T.

(b) After several measurements of the body’s temperature, it was determined that when the temperature of the body was 80 degrees, it was decreasing at the rate of 5 degrees per hour. Find k.

(c) Suppose that, at the time of death, the body’s temperature was about normal, say, 98°F. Determine f (t).

(d) When the body was discovered, its temperature was 85°F. Determine how long ago the person died.