Question 4.3 Rain starts falling on an empty swimming pool one hour after midday. At t hours after midday (for any real t z 1), the rate that rain water enters the pool is 128 / t2 litres per hour and the water leaks out of the pool at a rate of 2t litres per hour (until the pool is empty again). a) Find the time when the maximum amount of water is in the pool. b) Find an expression for the am0unt of water in the pool t hours after midday, that is valid for any t 2 1 until the pool is again empty. 0) Find the amount of water in the pool, when it is at its maximum. d) Show that the pool is not yet empty by 10pm on the same day