An ecologist is studying an island mhabited by three types of animal: puffins, turtles and lemurs. At the beginning of the year, the ecologist records that there is a total of 3000 animals on the island, and that the number of puffins and turtles combined is equal to four times the number of lemurs. Based on the animals' breeding habits, the ecologist predicts that by the end of the year: the population of puffins will have increased by 1.1% the population of turtles will have increased by 3.5% the population of lemurs will have decreased by 1.5% These changes mean that, by the end of the year, the total number of animals on the island will have increased by 51. (a) Model this situation as a matrix equation, where the unknowns represent the number of each type of animal present on the island at the start of the year. (2) (b) Find the number of each type of animal present on the island at the start of the year. (2) In fact, the population of animals at the start of the year was 3000 to the nearest 100. (c) Explain how this affects your answer to part (b). You do not need to perform any calculations. (2)