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6. Newton's Law of Cooling (Warming): The temperature I of an object at time t is given by the formula T(t) - T. + (T. - T.) e- kt where T(0) - T, is the initial temperature of the object, Ta is the ambient temperature" and k > 0 is the constant of proportionality which satisfies the equation (instantaneous rate of change of I'(t) at time t) = k (T(t) - Ta) "That is, the temperature of the surroundings. What determines if the function T(t) is increasing or decreasing is if 7, (the initial temperature of the object) is greater than 7. (the ambient temperature) or vice-versa. as we see in our next example. A 40"F roast is cooked in a 350'F oven. After 2 hours, the temperature of the roast is 125 F. 1. Assuming the temperature of the roast follows Newton's Law of Warming, find a formula for the temperature of the roast / as a function of its time in the oven, /. in hours. 2. The roast is done when the internal temperature reaches 165 F. When will the roast be done