Question

Any help appreciated, struggling with this one.

7. (9pts) A linear model for the population of cheetahs and gazelles in Namibia is given by the following pair of equations: where Ck measures the number of cheetahs present in a certain Namibian game reserve at time k, Gk gives the number of gazelles (measured in tens), and k is measured in months (a) Find a value for p (to three decimal places) that guarantees a steady-state outcome for this model, then determine the number of cheetahs present for every 1000 gazelles in the long-run. (b) Find a value for p (to three decimal places) that will guarantee 2% growth in both populations (c) What must be true about the eigenvalues of the transition matrix if both populations die out in the long-run?

Answer 1

IK kt 1k ieti Ik foov. Da@ 一tten 씬 0구 口-7

Jrowh) ㅏ.OLCK o. 3 (k+o--6k ohon vectos -P 1-3 rs eigen va