Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 1 - Section 1.3 - Linear Functions and Models - Exercises - Page 91: 84

Answer

$q=-50p+4200$

Work Step by Step

A demand function expresses demand $q$ (the number of items demanded) as a function of the unit price $p$ (the price per item). If it is a linear function, it has form $q=mp+b$. Given $(5,3950)$ and $(10,3700)$, two points on the graph, we find the slope: $m=\displaystyle \frac{3700-3950}{10-5}=\frac{-250}{5}=-50.$ So far, we have $q=-50p+b.$ Substitute the coordinates of $(5,3950)$ and solve for b. $3950=-50(5)+b$ $3950=-250+b\qquad/+250$ $4200=b$ Thus, $q=-50p+4200$
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