Problem 1: Newton's empirical law of cooling states that the rate at which the temperature of a body changes is proportional to the difference between the temperature of the body

and the temperature of the surrounding medium. Let T(t) represent the temperature of the body at time t and Tm denote the temperature of the surrounding medium at time t. (a) Set up a differential equation that models the system described above. (b) Consider the following scenario: At t = 0, a sealed tube containing a chemical is immersed in a liquid bath. The initial temperature of the chemical in the test tube is 80° F. The liquid bath has a controlled temperature given by Tm = 50° F. Use the model in part (a) to solve for the temperature of the chemical in the sealed tube in this scenario. Assume a proportionality constant of -0.1 and that time is measured in minutes.