Question

I am trying to use the theorem x_n=(Aⁿ ) (x_n-1 ) and (A-I)x=0 to figure it out but so far I have failed. Any help is appreciated.

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

AnsBien dota, the populatien chee s ond ge eltes oheng k+1 P+1.34 whesre Present& Cym 1.3 Ge

(a) a value Pe dateo mina he numben of Cheetoh aun Cye

ou P o.525 lang yun, numlesof ls looe 411-02C 102 1

Lt -12o re o.28 0.72メ0.28 : o-up -up 0.2016 ㄩ Gro

o-3 ou -p 1.3 Go Gp e on replate e maix by K Co Gro 1.3 KC This heplers f eigen valses are bsctasen o ond 1 O C