MATH 240 Final: MATH240 fall2009 Final MATH232-solution

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Instructions/remarks: read all instructions, the questions are on the 12 numbered single-sided pages following this one. Count them now: please include all details and rough work. You may use the back of the question pages and there is extra paper should you require it: the exam is out of a total of 100 marks. The value of each question is indicated below: no calculators or electronic devices of any kind are permitted, you have 3 hours to complete this examination, good luck! Question 1 [15pts] suppose the entire population of a certain nation lives either in the city or the country. 1 be the number of people living in the city in year k and let x(k) 2 be the number of people living in the country in year k. let x(k) =" x(k) 1 x(k: the model can be expressed as x(k+1) = ax(k). What is a: one of the eigenvalues of a is 1.