+ 8. (4 pts) The Leslie matrix for a female cheetah population with four age groups consisting of cubs, adolescents, young adults, and adults has largest eigenvalue c = 1.255 and associated eigenvector [30.5] 11.4 17.2 [80.3] a) What is true about the long-term fate of this population? A. The population dies out because the initial population is an eigenvector B. _The population dies out because the long-term growth factor c is less than 1 C. The population grows exponentially because the long-term growth factor c is positive D. _The population grows exponentially because the long-term growth factor c is greater than 1 E. The population stays the same because the initial population is not an eigenvector b) Determine the percentage of female cubs in the long run. Round the percentage to two decimal places. +16 9. (6 pts) 1.76Pn-1 A Beverton-Holt model is given by the DDS Pn = -and initial value Po = 110. 1+0.001Pn-1 a) Find the two equilibrium values of this model. Make sure to show your work. 1.26 P-1 1+0.001 Pul Po 2160 110 = (1.76 Pn-1) i+ 0.001 Pu-1) (0.26 pm 1) + (.001) Pa P = 6.26 The equilibrium values are 0 and 0.76 b) Iterations of the solutions of the model starting from Po = 810 and Po 740 are graphed on the right. Use the graph of the population sequences to determine the 820+ -800- stability of the non-zero 780- equilibrium value. Give a reason for your answer. --760 The non-zero equilibrium value is 4 -1 740 345 6 7 8 9 16 720+ because question is about stabilite