Problem

Interpret average rate $-2.5~(\text{dollars}~\text{per}~\text{item})~\text{per}~\text{item}$ on $10~\text{to}~20~\text{items}$. State the interval, signed rate and direction, per-added-item meaning, and total change in average cost.

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A signed average rate carries layered units: the output quantity here is already dollars per item, and that change is measured per added item. Use the sign for direction and the magnitude for the per-unit meaning. Multiplying by the interval width cancels the input unit and recovers the total change in average cost across the interval.

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Interval: 10 to 20 items. Rate: −2.5 dollars/item for the whole interval. Direction: average cost decreases. Per-unit meaning: no per-added-item rate. Total change: −$2.50 per item.

Interval: 10 to 20 items. Rate: −2.5 dollars. Direction: total dollars decrease. Per-unit meaning: item-count division is omitted. Total change: −$2.50 total.

Interval: 10 to 20 items. Rate: −2.5 (dollars/item)/item. Direction: average cost decreases. Per-unit meaning: $2.50 less per item for each added item. Total change: −$25 per item.

Interval: 10 to 20 items. Rate: +2.5 (dollars/item)/item. Direction: average cost increases. Per-unit meaning: $2.50 more per item for each added item. Total change: +$25 per item.

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Interpret average rate \(-2.5~(\text{dollars}~\text{per}~\text{item})~\text{per}~\text{item}\) on \(10~\text{to}~20~\text{items}\). State the interval, signed rate and direction, per-added-item meaning, and total change in average cost.

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