A bar of metal is cooling from 1000◦C to room temperature, 20◦C. The temperature, H, of the bar t minutes after it starts cooling is given, in ◦C, by

H = 20 + 980e^−0.1t.

(a) Find the temperature of the bar at the end of one hour.
(b) Find the average value of the temperature over the first hour.
(c) Is your answer to part (b) greater or smaller than the average of the temperatures at the beginning and the end of the hour? Explain this in terms of the concavity of the graph of H.