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Suppose you have just poured a cup of freshly brewed coffee with temperature 94 C...

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Calculus

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Suppose you have just poured a cup of freshly brewed coffee with temperature 94 C in a room where the temperature is 20 C a When do you think the coffee cools most quickly What happens to the rate of cooling as time goes by Explain The coffee cools most quickly as soon as it is removed from the heat source The rate of cooling decreases towards 0 coffee approaches room temperature b 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 provided that this difference is not too large Write a differential equation that expresses Newton s law of cooling for this particular situation Use t as the independent variable y as the dependent variable R as the room temperature and k as a proportionality constant dy k dt X What is the initial condition y 0 94 In view of your answer to part a do you think this differential equation is an appropriate model for cooling The answer and the model support each other because as y approaches R dy dt approaches 0 since the so the model seems appropriate

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