State Transition Matrix Model

Question

Two coffee shops, JavaJoy and BeanBrew, serve a small town. Each month, 15% of JavaJoy's customers switch to BeanBrew, and 25% of BeanBrew's customers switch to JavaJoy. Let $J_n$ and $B_n$ represent the number of customers at JavaJoy and BeanBrew, respectively, during month $n$. Which matrix equation correctly models $J_{n+1}$ and $B_{n+1}$, the number of customers at each shop during month $n+1$?

Accepted Answer

$$\begin{bmatrix} J_{n+1} \ B_{n+1} \end{bmatrix} = \begin{bmatrix} 0.85 & 0.25 \ 0.15 & 0.75 \end{bmatrix} \begin{bmatrix} J_n \ B_n \end{bmatrix}$$

Answer

$$\begin{bmatrix} J_{n+1} \ B_{n+1} \end{bmatrix} = \begin{bmatrix} 0.85 & 0.15 \ 0.25 & 0.75 \end{bmatrix} \begin{bmatrix} J_n \ B_n \end{bmatrix}$$

Answer

$$\begin{bmatrix} J_{n+1} \ B_{n+1} \end{bmatrix} = \begin{bmatrix} 0.75 & 0.15 \ 0.25 & 0.85 \end{bmatrix} \begin{bmatrix} J_n \ B_n \end{bmatrix}$$

Answer

$$\begin{bmatrix} J_{n+1} \ B_{n+1} \end{bmatrix} = \begin{bmatrix} J_n \ B_n \end{bmatrix} \begin{bmatrix} 0.85 & 0.25 \ 0.15 & 0.75 \end{bmatrix}$$

State Transition Matrix Model

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