Question: Suppose a cold object is placed into a room which is held at temperature T, and that the objects warms up according to Newton's law:
Suppose a cold object is placed into a room which is held at temperature T, and that the objects warms up according to Newton's law: y'(t)=k(t)(T-y(t)), where y(t) is the object's temperature, and k(t) depends on the physical properties of the object. The solution of this equation is y(t)=T-e-k(t)dt.Suppose k(t)=C, where C is an unknown positive constant. Suppose that object's temperature at time 1 is 20 degrees, temperature at time 4 is 22 degrees, and that the temperature of the room is held constant at 50 degrees. What was the objects temperature at time 0?
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