Problem

A parking garage charges exactly $\$15$ for any allowed stay length $h~\ge~0~\text{hours}$. Determine the most specific model family, equation and domain, rate, decisive evidence, and its relation to linear functions.

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family = constant; model = C(h)=15 for h≥0; parameters = fee 15 dollars and rate 0 dollars/hour; evidence = output remains $15 for every allowed input; relation = constant is linear with slope 0 but is most specific

family = linear; model = C(h)=15h for h≥0; parameters = rate 15 dollars/hour and initial fee 0; evidence = fee 15 appears in model; relation = constant cannot be linear

family = exponential; model = C(h)=15ᵍ for h≥0; parameters = factor 15 and initial fee 1 dollar; evidence = a repeated fee is multiplicative; relation = exponential is constant when h changes

family = quadratic; model = C(h)=-h²+15 for h≥0; parameters = maximum fee 15 and curvature -1; evidence = the fee has a maximum of $15; relation = quadratics are constant at their vertex

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A parking garage charges exactly \(\$15\) for any allowed stay length \(h~\ge~0~\text{hours}\). Determine the most specific model family, equation and domain, rate, decisive evidence, and its relation to linear functions.

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