Answer Happy

The Leslie matrix below describes a female cheetah population with four age groups consisting of cubs, adolescents, young adults, and adults, with an initial population that consists of 100 female adults: 0 0 2.3 2.8 0 0.06 0 0 0 L = and X (0) = 0 0.7 0 0 0 0 0 0.8 0.79 100 (a) If the largest eigenvalue of L is c = 1.25, what is true about the long-term fate of this population? O The population stays the same because the initial population is not an eigenvector O The population grows exponentially because the long-term growth rate c is positive O The population dies out because the long-term growth rate c is less than 1 O The population grows exponentially because the long-term growth rate c is greater than 1 O The population dies out because the initial population is an eigenvector (b) Assume that the general solution for the eigenvectors to the eigenvalue in (a) is given by (4.1z, 0.011z, 0.02z, z) What is the specific eigenvector when z = 20? (c) To compute the proportion of the adolescent females in the long run, you O Compute the population of adolescents at time n = 1 and divide by the initial number of adolescents. O Compute the population of adolescents at time n = 10 and divide by the initial number of adolescents. O Divide the second entry of the eigenvector by the sum of the entries of the eigenvector. O Write the second entry in the eigenvector in percentage form.