Newtons law of cooling states that if an object with temperature t(t) at time t is in a medium with temperature tm the rate of change of t at time t is proportional to t(t) − tm, thus t satisfies a differential equation of the form t 0 = −k(t − tm) here k > 0, since the temperature of the object must decrease if t > tm, or increase if t < tm. well call k the temperature decay constant of the medium. (a) a thermometer is moved from a room where the temperature is 70f to a freezer where the tem- perature is 12f . after 30 seconds the thermometer reads 40f. what does it read after 2 minutes? (b) an object is placed in a room where the temperature is 20c. the temperature of the object drops by 5c in 4 minutes and by 7c in 8 minutes. what was the temperature of the object when it was initially placed in the room?
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