36   14. (a) Express 3 2 1 1 ( )( ) x x − + in partial fractions. (3) When chemical A and chemical B are mixed, oxygen is produced. A scientist mixed these two chemicals and measured the total volume of oxygen produced over a period of time. The total volume of oxygen produced, V m 3 , t hours after the chemicals were mixed, is modelled by the differential equation d d V t = 3 2 1 1 V t t ( )( ) − + V  0      t  k where k is a constant. Given that exactly 2 hours after the chemicals were mixed, a total volume of 3 m 3 of oxygen had been produced, (b) solve the differential equation to show that V = 3 2 1 1 ( ) ( ) t t − + (5) The scientist noticed that • there was a time delay between the chemicals being mixed and oxygen being produced • there was a limit to the total volume of oxygen produced Deduce from the model (c) (i) the time delay giving your answer in minutes, (ii) the limit giving your answer in m 3 (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 37   Question 14 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________