Newton’s Law of Cooling is y = ae^(-kt) + c. The formula relates a substance’s temperature, y, to the time, t, in minutes that it has spent cooling.

Suppose a sample of a substance is heated in a container of boiling water until its temperature is 100° C. The sample is cooled by being left in a room of 24° C. The value a equals the difference between the sample’s initial temperature and the surrounding temperature. The value c represents the surrounding temperature. The cooling constant of the substance is k = 0.12. Find the sample’s temperature after 20 minutes.

Question

Newton’s Law of Cooling is y = ae^(-kt) + c. The formula relates a substance’s temperature, y, to the time, t, in minutes that it has spent cooling.


Suppose a sample of a substance is heated in a container of boiling water until its temperature is 100° C. The sample is cooled by being left in a room of 24° C. The value a equals the difference between the sample’s initial temperature and the surrounding temperature. The value c represents the surrounding temperature. The cooling constant of the substance is k = 0.12. Find the sample’s temperature after 20 minutes.

anonymous · Answer

a. 30.9 degrees C
b. 33.1 degrees C
c. 11.1 degrees C
d. 26.2 degrees C