The temperature of a room, in degrees Fahrenheit, on a certain day is modeled by the function f defined at the right, where g is a differentiable function and tis measured in hours since midnight. Values of g(t) at selected values of t are given in the table at the right. f(t) = g (t) -3t+83 t (hours) g(t) (degrees Fahrenheit) for 0 ≤ t ≤ 12 for 12 < t < 24 0 4 87 81.5 6 76 a. According to the data table of f what is the average rate of change of temperature of the room over the time interval 0 ≤ t ≤ 12 hours? b. Isf continuous for 0 ≤ t ≤ 24 hours? Justify your answer. in degrees c. Find f'(20), the instantaneous rate of change in the temperature of the room, Fahrenheit per hour, at time t = 20 hours. Interpret your answer in context using one sentence. 8 70.5 12 65

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