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An ornithologist is studying a population of female sparrows as it changes each year. They are assuming the following things about this bird population: 0-year old sparrows (0 - 1-year old sparrows (1- 2-year old sparrows (2- 3-year old sparrows (3 - 4 years) 1 year) 2 years) 3 years) Does not lay eggs Has 0.75 female offspring each Has 0.5 female offspring each Has 1 female offspring each 35% survive to become 1-year olds 75% survive to become 2-year olds 70% survive to become 3-year olds None survive to become 4-year olds (a) (1 point) Find the Leslie matrix A for this population of sparrows. A =
20 10 (b) (5 points) Assume the initial population is given by . Go to the Leslie Matrix Calculator, enter 40 45 the information, and submit the matrix. Take one or more screen shots that shows the matrix information you entered, the population graph, the proportion graph and the eigenvalue/eigenvector information. Upload the screen shot(s) as a picture. Then answer the following questions: i) What is the largest eigenvalue of this Leslie matrix? ii) What will happen to the population in the long run? Give a reason. iii) What is the proportion of the 3-year old sparrows in the long run? Write your answer as percentage with one decimal place and explain how you got your answer. You can either write your answers by hand and then upload your work (as another picture) or you can type the answers into the window. For part (b), the screen shots, each numerical answer, and your explanations are worth one point each. Edit Insert Formats BIU X₂ x² A A 블 Σ+ Σ Α .