Question

1. Thought extinct since 1924, the Canterbury knobbled weevil was rediscovered in 2004 inhabiting golden speargrass in Burkes Pass, South Canterbury. The population of knobbled weevils is very small and changes on a yearly basis as a discrete dynamic system. Suppose that initially there are 30 30 juvenile chicks and 20 breeding adults, that is Xo = Suppose also that the yearly transition 20 Gs 1.25) matrix is A- 0.75 0.5 (a) Which entry in the transition matrix gives the annual birthrate of chicks per adult? (b) Which entry tells us the proportion of chicks that will survive to become adults? (c) Calculate the state vector x1 (d) Find the eigenvalues and corresponding eigenvectors for matrix A. (e) Express Xo as a linear combination of eigenvectors (f) Find the long-term distribution, after n years. State the long term ratio of juveniles to adults (g) From your result to part (f), is the knobbled weevil likely to survive?

Answer 1

Answer o 2s 30 2D l a e e Juvenile chicks ,a-30 ler 、b' be the breeding adults , b: 20 Since auo,n2, a30 S ,a23-0 s. where the transth mati>x chicrs pes aoult a21二0.75 ,enku talls us Hne PYOPOtior chicks thot wil survive b become adults 30 x, n 1 0x30ナ1.25x20

32S 32.S hence charactaristic ejuah onić Thus the va lve the ege vales ae r 1,25-0 ,75 let 125

3 -125 0.75 05 1.25 1.23 거 メ:0 0.75-0.75 So the above matit Sottar from equaが&JO and @ ue 9r