A rectangular swimming pool is 20 metres long and 6 metres wide. It has a depth of 1 metre at the shallow end, but eventually slopes to a depth of 1.5 metres at the deep end as illustrated in the picture below. The pool is being filled with a hose at a rate of 50,000 cubic centimetres per minute. (a) Let \( h(t)\) denote the height of the water in the pool at time \( t \). Without doing any computations, analyze the concavity of the graph of \( y=h(t)\). Where do you expect the graph to be concave up? Where do you expect the graph to be concave down? Are there any intervals where the graph is neither concave up nor concave down? Explain. At what rate is the water rising 2 hours after the hose is turned on? Give your answer in metres per minute and show all your work. Include diagrams, introduce your notation, and fully explain your workings step by step. At what rate is the water rising 6 hours after the hose is turned on? Give your answer in metres per minute and show all your work. Include diagrams, introduce your notation, and fully explain your workings step by step.