Total cost $C(n)$, in dollars, has average rate of change $\$12~\text{per}~\text{item}$ from $n~=~1$ to $n~=~6~\text{items}$. Calculate the input and output changes, state the units, and interpret the average rate and total change in context.

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input change = 6-1=5 items; average rate = +$12/item; output change = 12·5=+$60; meaning = from 1 to 6 items, total cost increases $60, averaging $12 per additional item

input change = 5 items; rate = +$12/item; output change = +$12 total

input change = 7 items; rate = +$12/item; output change = +$84

input change = 5 items; rate = 12 items/dollar; output change = $5/12

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Curriculum context

Course: Math I
Standard: F-IF.6
Category: Functions
Domain: Interpreting Functions
Objective: Calculate, estimate, and interpret average rate of change over an interval.
Problem type: Interpret average rate of change with units

Total cost \(C(n)\), in dollars, has average rate of change \(\$12~\text{per}~\text{item}\) from \(n~=~1\) to \(n~=~6~\text{items}\). Calculate the input and output changes, state the units, and interpret the average rate and total change in context.

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