Combine standard function types arithmetically to create models.
Form and interpret a quotient function to model an average or unit rate
Problem
A business's total cost for \(n\) orders is \(C(n)=50n+100~\text{dollars}\). Form and simplify the average-cost function \(A(n)=C(n)/n\). State its units, distinguish the algebraic restriction from the positive-integer order domain, and interpret \(50+100/n\) in context.
Big Picture
What this problem is really about
Average cost divides the entire total-cost output by the number of orders. We’ll group the full numerator, simplify both terms for nonzero input, derive dollars-per-order units, distinguish the algebraic restriction from the positive-integer contextual domain, and interpret the variable and allocated fixed-cost portions.
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