In an experiment, a test tube containing a chemical is immersed in a water bath. At t = 0, the temperature, H (t) of the chemical in the test tube is 27°C. The controlled temperature (measured in degrees Celcius) of the water bath is Hw (t) = 38– 22e-0.1", t > 0, where t is measured in minutes. Referring to the Newton's empirical law = k (H – Hw), where k is the proportionality constant assumed to be -0.1 per minute, answer the following questions: HP dt In words, discuss the profile of the temperature H (t) in the short term AND in the long term (Calculation is not needed). (i) (ii) Solve this initial value problem.

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