Suppose you have just poured a cup of freshly brewed coffee with temperature 90 C in a room where the temperature is 25 C Newton

Question

Suppose you have just poured a cup of freshly brewed coffee with temperature 90 C in a room where the temperature is 25 C Newton s Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings Therefore the temperature of the coffee T t satisfies the differential equation A What is the limiting value of the temperature of the coffee where Troom 25 is the room temperature and k is some constant Suppose it is known that the coffee cools at a rate of 1 C per minute when its temperature is 75 C lim T t tx B What is the limiting value of the rate of cooling dT lim t 00 dt C Find the constant k in the differential equation k EB dT dt CER k T Troom D Use Euler s method with step size Ax 3 minutes to estimate the temperature of the coffee after 15 minutes

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