Use Newton's Law of Cooling to find the temperature of a substance as a function of time t in minutes that it has spent cooling off. This relationship is given by, y = ae ^-kt+ C, where c is the temperature of the medium surrounding
the cooling object, a is the difference between the initial temperature of the object and the surrounding temperature,
and k is a constant related to the cooling object. Two samples of the substance were heated in a container of
boiling water until their initial temperatures were both 100°C. The first sample will be cooled by being left out at a
room temperature of 24°C, and the second sample of the substance will instead be cooled off in a refrigerator with
an inside temperature of 4°C. The value of a will equal the difference between each sample's initial temperature
and that sample's surrounding temperature, and the cooling constant of the substance is k = 0.12.
a. Find the first sample's temperature after it has cooled for 20 minutes.
b. Find the second sample's temperature after it has cooled for 10 minutes.