A pot of boiling water (212◦ F) is left to cool in a room that is 70◦ F. Newton’s Law of Cooling states that the temperature of the water t minutes after it was left to cool will be T(t) = 70 − Ae^-kt degrees F, where A and k are some constants. After 10 minutes, you measure that the water has cooled to 180◦ F.

(a) Find A and k.

(b)When will the water reach a temperature of 90◦ F?

(c)At what rate is the temperature of the water changing when t = 20?