Selecting a model (linear vs quadratic vs exponential)
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A gym charges a one-time sign-up fee plus a fixed monthly rate. The total amount paid (in dollars) after \(x\) months is shown below. \[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Months } x & 0 & 1 & 2 & 3 & 4 \\ \hline \text{Total } y & 40 & 75 & 110 & 145 & 180 \\ \hline \end{array} \] State whether the data is best modeled by a \(\textbf{linear}\), \(\textbf{quadratic}\), or \(\textbf{exponential}\) function, and justify your choice.
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