(1 mark) At the beginning of month 71., an existing population of cockroaches X\" is sprayed with an insecticide whose instant kill-rate is 90%. Of those that survive, 60% run away and never return. Before the end of the month, 500 new cockroaches join the population. The difference equation that models the population of cockroaches is: a) AX = 0.96Xn + 500 b) Xn+1 = 0.96Xn + 500 c) Xn+1 = 0.0437,; + 500 d) AX = 0.04Xn + 250 e) AX = 0.04Xn + 500