Problem

For \(S(x)~=~100x/(x~+~20)\), where \(x~\ge~0\) is in input-units and \(S\) is saturation percent, give the exact base-plus-correction form, state the correction limit, identify the asymptote, and explain the direction of approach.

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Rewrite: 100 − 2000/(x + 20). Correction: −2000/(x + 20) → 0. Asymptote: slant, y = 100x. Context: saturation grows without bound as input grows.

Rewrite: 100 + 2000/(x + 20). Correction: 2000/(x + 20) → 0. Asymptote: horizontal, y = 100. Context: saturation approaches 100 percent from above as input grows.

Rewrite: 80 + 1600/(x + 20). Correction: 1600/(x + 20) → 0. Asymptote: horizontal, y = 80. Context: saturation approaches 80 percent from above as input grows.

Rewrite: 100 − 2000/(x + 20). Correction: −2000/(x + 20) → 0. Asymptote: horizontal, y = 100. Context: saturation approaches 100 percent from below as input grows.

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For \(S(x)~=~100x/(x~+~20)\), where \(x~\ge~0\) is in input-units and \(S\) is saturation percent, give the exact base-plus-correction form, state the correction limit, identify the asymptote, and explain the direction of approach.

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