Please and Please sophisticated and detailed and step by step answers it is for my pre calculus 12 class ???

4. The rate at which liquids cool can be modeled by an approximation of Newton's law of cooling T(t) = (T, - T)(0.9)# + T, where I, represents the final temperature, in degrees Celsius; T, represents the initial temperature, in degrees Celsius; and t represents the elapsed time, in minutes. a) Sketch a graph showing a cup of coffee with initial temperature of 90 C that cools down to room temperature of 20 C over a period of 200 min. You may use technology, but make sure you label the axis! b) What is the approximate temperate of coffee after 120 min? c) Determine the horizontal asymptote. What does it represent in this situation? d) What does 0.9 from the equation represent in this situation