Problem

A quantity starts at \(50\) and doubles each period \(t\). Model A is \(50+2t\), and Model B is \(50(2)^t\). Evaluate \(\text{both}~\text{models}\) against the context. Report the valid model, the governing relationship, the feature that matches, and the mismatch in the rejected model.

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selected model=A; governing relationship=constant change of2 per period; feature match=50 is the initial value and2 is the slope; rejected-model mismatch=B has a changing rate rather than a constant rate

selected model=B; governing relationship=multiply50 by2t; feature match=2t means2 times t; rejected-model mismatch=A adds2t instead of multiplying50 by2t

selected model=A; governing relationship=doubling means add2 each period; feature match=2t records one addition of2 per period; rejected-model mismatch=B multiplies by2 instead of adding2

selected model=B; governing relationship=multiply by2 each period; feature match=exponential factor2t with initial value50; rejected-model mismatch=A adds2 each period

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A quantity starts at \(50\) and doubles each period \(t\). Model A is \(50+2t\), and Model B is \(50(2)^t\). Evaluate \(\text{both}~\text{models}\) against the context. Report the valid model, the governing relationship, the feature that matches, and the mismatch in the rejected model.

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