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: 83

Answer

$q=-40p+2000$

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 $(1,1960)$ and $(5,1800)$, two pints on the graph, we find the slope: $m=\displaystyle \frac{1800-1960}{5-1}=\frac{-160}{4}=-40.$ So far, we have $q=-40p+b.$ Substitute the coordinates of $(1,1960)$ and solve for b. $1960=-40(1)+b\qquad/+40$ $2000=b$ Thus, $q=-40p+2000$
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