Newton's Law of Cooling The temperature, F(t), of a heated object at time t is given by F(t) = C + (To - C)e^kt,
where C is the constant temperature of the surrounding medium, To is the initial temperature
of the heated object, and k is a negative cooling constant that is associated with the object.
(a) Suppose a freshly brewed cup of coffee is 170° F and sits in a room with a constant
temperature of 68°. After 30 minutes the temperature of the coffee is 90°. Use Newton's
Law of Cooling to find a model for the temperature of the coffee, F(t), after t minutes.
(Hint: You need to find the constant k.)
(b) What is the temperature of the coffee after 45 minutes?
(c) When will the temperature of the coffee be 100°?
(d) Calculate the inverse F^-1(x) of F(t). In the context of the question, what consists of the
domain of the inverse and what is the range? That is, what does F^-1 (2) model?