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.
