[Maximum mark: 7] A simple model to predict the population of the world is set up as follows. At time t years the population of the world is x, which can be assumed to be a continuous variable. The rate of increase of x due to births is 0.056): and the rate of decrease of x due to deaths is 0.035x. (a) Show that % = 0.021x. [1] (b) Find a prediction for the number of years it will take for the population of the world to double. [6]