Precalculus · Problem 5.1.63

Further Topics in Functions — Stitz & Zeager

Mathematics — Precalculus · function-composition-application

Problem

Suppose a local vendor charges \2perhotdogandthatthenumberofhotdogssoldperhour2 per hot dog and that the number of hot dogs sold per hour xisgivenby is given by x(t) = -4t^2 + 20t + 92,where, where tisthenumberofhourssince10AM, is the number of hours since 10 AM, 0 \leq t \leq 4$. (a) Find an expression for the revenue per hour RR as a function of xx. (b) Find and simplify (R∘x)(t)(R \circ x)(t). What does this represent? (c) What is the revenue per hour at noon?

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