Background Information: Eight ounces of coffee is brewed into a ceramic mug and has an initial temperature, To, of 194F. After brewing, the coffee mug is placed on the kitchen counter where the room temperature, Ts, is 74F. Suppose that the temperature of the coffee, T, after, t, minutes is given by: T(t)=Ts+(ToTs)ebt where b is the heat transfer coefficient of 0.0311. Objective: Use MATLAB to numerically analyze the following questions. 1. Create a vector of t with a range of [0,180] and calculate the corresponding T vector (i.e., let t be the input variable and T be the output variable). 2. Plot a graph of T(t). 3. Visually, inspect T(t) and determine when the coffee begins to approach room temperature? 4. The drinking temperature for coffee has a range of [125,155]F. When should the coffee be consumed? 5. Describe how cooling temperature might differ if the coffee was brewed in an insulated cup