Question 1 (8 marks) The population of a bacteria (P, 'thousand') after 't' hours can be modelled using the function: P(t) = 7 x 1. 8(1.21-4) a) Determine the population of the bacteria after 9 hours (to 3 sig. fig.). (2 marks) b) Approximate the instantaneous rate at which the population is growing after 9 hours, using the interval [9, 9.1]. (3 marks) c) Briefly comment on the accuracy of your answer in (b), by considering a smaller interval (at least 10 times smaller). (3 marks) Question 2 (9 marks) a) Evaluate the following limits: (2, 2, 3) (i) lim 5x2h-10h2+3h (ii) lim 2(3+h)2-2x(3)2 (i1) lim 3h2-h-10 h-0 h h-0 h h-2 h 2- 4 b) Briefly comment on what the process in (ii) above is finding. (2 marks) Question 3 (8 marks) An object moved in a straight line such that its distance from a point 'O' is given by the function: S(t) = +3 - 10t2 + 24t + 11 a) Determine the average rate of change of the object from 'O' with respect to time, for the time interval [3, 9]. (2 marks) b) Estimate the instantaneous rate of change of the object from 'O' with respect to time, at t = 6, using an appropriate interval centred at t = 6. (3 marks c) Determine the objects instantaneous speed when t = 6, using the interval [6, 6 + h] and limits. (3 mark