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[20 marks] Question 1 Consider a Leslie model of a population with three age groups, 0-1 year, 1-2 years, and 2-3 years. Assume that the fecundity rates of the first and second age group are 0 and the fecundity rate of the third age group is 72. The survival rate from the first to the second age group is 75% and the survival rate from the second to the third age group is 50%. (a) Write out the Leslie matrix L for this model. (b) Find the inverse matrix of L and hence determine the population vector one year ago if the current population consists of (72, 18, 3) individuals in the first, second and third age group (c) Find the real eigenvalue and the corresponding eigenvector of L. (d) Does the population become extinct, stay steady or grow? Justify your answer.

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