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- Paper 2 dp2 december updated - Word (Coon akTneaunn nponykTa) PA3METKA CTPAHNLbl CCbinky PACCbInKN PELLEH3NPOBAHNE BVIA .1 .1 . 1 .2 . 1 . 3 . 1 . 4 . 1 . 5 . 1 . 6 . 1 . 7 . 1 . 8 . 1 . 9 . 1 . 10 . 1 . 11. 1 .12 . 1 13 . 1 . 14 . 1 . 15 . 1 1 17 18 3. [Maximum mark: 17] A biologist introduces 100 rabbits to an island and records the size of their population (x) over a period of time. The population growth of the rabbits can be approximately modelled by the following differential equation, where r is time measured in years. dx _2x dr (a) Find the population of rabbits 1 year after they were introduced. [5] A population of 100 foxes is introduced to-the island when the population of rabbits has reached 1000. The subsequent population growth of rabbits and foxes, where y is the population of foxes at time r, can be approximately modelled by the coupled equations = x(2 - 0.01y) =)(0.0002x - 0.8) (b) Use Euler's method with a step size of 0.25, to find (1) the population of rabbits 1 year after the foxes were introduced