(Solved): According to demographic studies, the number of spotted owls in the Pacific Northwest satisfies the ...

According to demographic studies, the number of spotted owls in the Pacific Northwest satisfies the following difference equation. Where \( x_{k}, y_{k} \) and \( z_{k} \) denote the number of owls in the juvenile, subadult and adult stages at year \( k \), respectively. \[ \left[\begin{array}{l} x_{k+1} \\ y_{k+1} \\ z_{k+1} \end{array}\right]=\left[\begin{array}{ccc} 0 & 0 & 0.3 \\ 0.2 & 0 & 0 \\ 0 & 0.8 & 0.9 \end{array}\right]\left[\begin{array}{l} x_{k} \\ y_{k} \\ z_{k} \end{array}\right] \] If the total population of spotted owls in the Pacific Northwest is 1700 pairs, with following distribution: juvenile \( -60 \% \), subadult \( -10 \% \) and adult - \( 30 \% \) stages what is the total population of spotted owls in the Pacific Northwest expected in the next 100 years. Plot population of spotted owls in the Pacific Northwest over period of 100 years. At the 100 -year mark what is the total population? What is the distribution?