Problem

For \(T(n)~=~(4n^2~+~18)/(n~+~3)\), where \(n\) is a positive whole number of repairs and \(T\) is minutes, divide to obtain the exact trend-plus-correction form, state the correction limit, identify the asymptote, and interpret the rate.

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Rewrite: 4n + 12 − 18/(n + 3). Correction: −18/(n + 3) → 0. Asymptote: slant, T = 4n + 12. Context: total time follows a 4-minute-per-repair trend for many repairs.

Rewrite: 4n − 12 + 54/(n + 3). Correction: 54/(n + 3) → 0. Asymptote: horizontal, T = 4. Context: total repair time approaches 4 minutes for many repairs.

Rewrite: 4n − 12 + 18/(n + 3). Correction: 18/(n + 3) → 0. Asymptote: slant, T = 4n − 12. Context: total time follows a 4-minute-per-repair trend for many repairs.

Rewrite: 4n − 12 + 54/(n + 3). Correction: 54/(n + 3) → 0. Asymptote: slant, T = 4n − 12. Context: total time follows a 4-minute-per-repair trend for many repairs.

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For \(T(n)~=~(4n^2~+~18)/(n~+~3)\), where \(n\) is a positive whole number of repairs and \(T\) is minutes, divide to obtain the exact trend-plus-correction form, state the correction limit, identify the asymptote, and interpret the rate.

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