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(Solved): Water is boiled in a cup and cooled in a room that is at 27C. Assume that Newton's Law of Cooling ...



Water is boiled in a cup and cooled in a room that is at 27°C. Assume that Newton's Law of Cooling is satisfied: the rate of change of the water temperature at any time is proportional to the difference between the water temperature and the ambient temperature. Water boils at 100°C. We take the temperature of the water after 3 minutes and find that it is 87°C. (a) Set up and solve an Initial Value Problem to express the temperature of water as a function of time. (b) Sketch a graph of this function. (c) Calculate when the temperature of the water reaches 50°C.


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(a) Let's denote the temperature of the water at time t by T(t) . According to Newton's Law of Cooling, the rate of change of T(t) is proportional
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