Q2 (20 points) Water is being poured into a container in such a way that the height of the water at time t is H(t) = B(1 - e 3)173, where B is some constant (a) Show that the height of the water approaches (but never quite reaches) some maximum height H What is H? = 0.95 H? Express your answer in terms of Balone. (b) At what rate is the height of the water increasing when it is at height Ho (c) By inverting the function H, find the time T(h) at which the height of the water is h. (d) Assume now that B = 0.4. When the height of the water is Ho, approximately how long does it take for the height to increase by 0.001? Calculate your answer numerically, to four significant figures, in two ways: () by computing T(Ho +0.001) T(H) directly, using your answer to part (c). (ii) by differentiating both sides of the equation T(H(t)) = t with respect to t and using your answer to part (b)