At t = 0 a sealed test 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 (measured in degrees Fahrenheit) given by Tm(t) = 100 - 40e^-0.1t, t ≥ 0, where t is measured in minutes.

(a) Assume that k = -0.1 in (2). Before solving the IVP, describe in words what you expect the temperature T(t) of the chemical to be like in the short term. In the long term.

(b) Solve the initial-value problem. Use a graphing utility to plot the graph of T(t) on time intervals of various lengths. Do the graphs agree with your predictions in part (a)?