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A cup of coffee has a temperature of 80∘C when it is placed outside where the temperature is 20∘C. Suppose the temperature of the coffee, T(t), changes according to Newton's Law of Cooling with proportionality constant k = 0.09. (a) Find and classify the equilibrium solution(s) using a phase line. (b) Find T(t). (c) Evaluate and interpret limt→∞ T(t). (d) How long will it take for the coffee to reach a temperature of 25∘C ? How long to reach a temperature of 20∘C ?

A cup of coffee has a temperature of 80∘C when it is placed outside where the temperature is 20∘C. Suppose the temperature of the coffee, T(t), changes according to Newton's Law of Cooling with proportionality constant k = 0.09. (a) Find and classify the equilibrium solution(s) using a phase line. (b) Find T(t). (c) Evaluate and interpret limt→∞ T(t). (d) How long will it take for the coffee to reach a temperature of 25∘C ? How long to reach a temperature of 20∘C ?

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A cup of coffee has a temperature of 80 ∘ C when it is placed outside where the temperature is 20 ∘ C . Suppose the temperature of the coffee, T ( t ) , changes according to Newton's Law of Cooling with proportionality constant k = 0.09 . (a) Find and classify the equilibrium solution(s) using a phase line. (b) Find T ( t ) . (c) Evaluate and interpret lim t → ∞ T ( t ) . (d) How long will it take for the coffee to reach a temperature of 25 ∘ C ? How long to reach a temperature of 20 ∘ C ?

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