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State Transition Matrix Model
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A small town has two coffee shops: JavaJoy and BeanBrew. Each month, 15% of JavaJoy customers switch to BeanBrew, while 25% of BeanBrew customers switch to JavaJoy. If JavaJoy currently has 300 customers and BeanBrew has 200 customers, which matrix equation correctly models this situation?

A

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

B

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

C

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

D

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

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