Water is boiled in a cup and put to cool in a room that is 29 C.
Assume that Newton's Law of Cooling is satisfied: the rate of change of the temperature of the water at any time is proportional to the difference between the temperature of the water and the temperature of the environment.
Water boils at 100∘C. We take the temperature of the water after 9 minutes and find that it is 70∘C.
(a) Set up and solve an Initial Value Problem to express the water temperature as a function of time.
(b) Draw a graph of this function.
(c) Calculate when the water temperature reaches 31∘C.