So I was going through the old exam papers and found this question. I tried to look for a something a bit similar to this but found nothing. It was hinted that a similar question might appear in this year's exam so if anybody can help me then it'd be greatly appreciated. The question is as follows:
A study of a colony of a rare sea bird, the fairy tern, indicates that the population changes on a yearly basis as a discrete dynamic system. Dividing the population into 2 classes, juveniles and adults, there are initially 40 juvenile chicks and 20 breeding adults. The system is defined by: (1) an initial state vector x0 = (40 j
and (2) a transition matrix
A = (0 1.1
and (3) the relationship x(n+1) = A*x(n)
(a) Calculate the state vector x1.
(b) Which entry in the transition matrix gives the annual birthrate of chicks per adult?
(c) Which entry of A tells us the probability a chick will survive to become a breeding adult?
(d) Find the eigenvalues n' corresponding eigenvectors for matrix A.