Apply and reverse a state recurrence with external change
A quarterly nursery model records plants held at two propagation sites
Use the state order glasshouse site then shade-house site. State matrices are columns. In T, columns are current states and rows are next states. One application represents one quarter
The transition occurs first. The signed external-change column is applied afterwards. Positive entries of B add to a state and negative entries remove from a state
\[T=\begin{bmatrix} 0.8 & 0.4 \\ 0.2 & 0.6 \end{bmatrix}\]
\[S_{n+1}=T S_n+B\]
After each transition, an external intake adds 3 plants to shade-house site
\[B=\begin{bmatrix} 0 \\ 3 \end{bmatrix}\]
\[S_{1}=\begin{bmatrix} 45 \\ 30 \end{bmatrix}\]