1. (3 marks) Chloe learnt from her class to use difference equations to model the population growth of an isolated group of rabbits in two years, and she would like to apply a similar model to describe the population growth of cockroaches in an apartment. She assumed that there was one pair of cockroach larvae (i.e. baby cockroach), one of each gender, and two pairs of matured cockroaches, two of each gender, in the apartment at the beginning of January 2018. She checked that all cockroach larvae mature into adulthood in one month, after which a couple of matured cockroaches would produce 56 pairs (with equal number in each gender) of cockroach larvae every month. That means, at the beginning of March, 2018, the mentioned pair of cockroach larvae would have turned into adult and started reproducing, while the mentioned two pairs of adult cockroaches would have reproduced once by the beginning of February, 2018 and would keep on reproducing in the subsequent months. Assuming that all the cockroaches in the apartment would not die, how many pairs of cockroaches (adult cockroaches as well as larvae) would there be approximately (correct to 3 significant figures) in the apartment at the beginning of January, 2021? (A) 3.70 x 1032 (B) 2.93 x 1033 (C) 1.64 x 1034 (D) 2.37 x 1034 (E) None of the above