Suppose that sand is stored in a large bag, but at time t = O the bag develops a leak. The amount of sand 5' (measured in kilograms) in the bag at time t (measured in minutes) can be modeled by the following function: 5.02413), ,9: where K is a positive constant and p: is a positive constant called the coarseness constant of the sand. The domain of S is [0.1"] where T is the time when the bag becomes empty. 1. (a) [1 mark) How much sand was in the bag when it started leaking? Your answer may involve K and/or p5. You should specify units. (b) [1 mark) How fast is the sand leaking from the bag at time t minutes? Your answer may involve K and/or p5. You should specify units. (c) [2 marks) For this part only, suppose p: = 6. At time t = 2 minutes, is the rate at which sand is leaking from the bag speeding up or slowing down? Why? Support your answer with some computations and a written explanation. 2. (a) [1 mark) How long does it take for all of the sand to leak out? Your answer may involve K and/or pa. You should specify units. (b) [1 mark) Use your answers to Q1(b) and Q2(a) to check that 035' 1' = 0 tlrrii'l- dt [Remember that T is the time when the bag becomes empty.) Does this limit being zero make physical sense? Write a sentence explaining why or why not