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Piece-wise model with system of equations

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Hello, I am trying to develop a piece-wise model. Normally I would just use a matrix with i+1 and i. In this case however there is a system of equations that needs to be solved for each piece. I was using the 'given' and 'find' operators for the system of equations but I can't figure out how to do integrate this process with a step-wise procedure. Please find attached my file. I solved the first few pieces by hand just to illustrate more clearly what I am trying to do. Thanks!


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