Turn over 39  Question 13 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 13 is 6 marks) 40   14. 8 m 3 m h m 5 m T Figure 5 Water flows at a constant rate into a large tank. The tank is a cuboid, with all sides of negligible thickness. The base of the tank measures 8 m by 3 m and the height of the tank is 5 m. There is a tap at a point T at the bottom of the tank, as shown in Figure 5. At time t minutes after the tap has been opened • the depth of water in the tank is h metres • water is flowing into the tank at a constant rate of 0.48 m3 per minute • water is modelled as leaving the tank through the tap at a rate of 0.1h m3 per minute (a) Show that, according to the model, 1200 d d h t = 24 – 5h (4) Given that when the tap was opened, the depth of water in the tank was 2 m, (b) show that, according to the model, h = A + B e–kt where A, B and k are constants to be found. (6) Given that the tap remains open, (c) determine, according to the model, whether the tank will ever become full, giving a reason for your answer. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________