Suppose the population of a particular endangered bird changes on a yearly basis as a discrete dynamic system. Suppose that initially there are 60 juvenile chicks and 30 60 breeding adults, that is xo = [\begin{array}{c}60\\30\end{array}\right]
Suppose also that the yearly transition matrix is
A = [\begin{array}{cc}0&1.25\\s&0.5\end{array}\right]
where s is the proportion of chicks that survive to become adults (note 9 S 0.5 that 0≤ s≤ 1 must be true because of what this number represents).

(a) Which entry in the transition matrix gives the annual birthrate of chicks per adult?
(b) Scientists are concerned that the species may become extinct. Explain why if 0 ≤ s < 0.4 the species will become extinct. (c) If s = 0.4, the population will stabilise at a fixed size in the long term. What will this size be?