Based on the year 2000, Australia's population, P is expected to grow according to the function: P = 19.5 e 0.0163t where P is measured in millions, and t is the number of years since the year 2000. (a) Sketch the function over a one-hundred-year period, beginning in 2000. Plot your graph in steps of 10 years on the horizontal axis. Give your graph an appropriate title. (2 marks) (b) From your graph, determine the approximate number of years that it will take for the Australian population to double. (1 mark) (c) Rearrange the equation P = 19.5 e 0.0163t to make t the subject. (3 marks) (d) What type of function is the inverse of P = 19.5 e0.0163t ? (1 mark)