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 juvenile chicks and 20 breeding adults, that is xo- 30 Suppose also that the yearly transition 0 1.25 0.75 0.5 matrix is A 0 a) Which entry in the transition matrix gives the annual birthrate of chicks per adult? 1 mark b) Which entry tells us the proportion of chicks that will survive to become adults?1 mark 2 marks 5 marks 3 marks (f) Find the long-term distribution, after n years. State the long term ratio of juveniles to adults. 4 marks 2 marks (e) Calculate the state vector x (d) Find the eigenvalues and corresponding eigenvectors for matrix A. (e) Express xo as a linear combination of eigenvectors. (g) From your result to part (f), is the knobbled weevil likely to survive?

Answer 1

Please UPVOTE if this answer helps you understand better.

Solution:-

ao uwie chic 20 1.2S A: n (a) la,2-t.asi > 3A aǐw.the ammual biMhrodeo chicks pes adul 0 1-25 25 107s o, s 0x30ナ1.25 x 20 ) : /25 25 S 30+05x 2 32 5 (4) .76

1.25 ] /지 ク( +0.25 1.25 1.25/ 24

ウ 30 2

2 o s 3 2 2 43(3x32-2 2
(g) For the Ratio that we got in part (f), even we check for n=1, we get this ratio is less than 1. Also, as n increases, this ratio decreases continuously, if it goes continue, those juvenile chicks won't survive.

Please UPVOTE if this answer helps you understand better.