Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.7 - Variation and Problem Solving - Exercise Set - Page 397: 25


reduces by $ \dfrac{1}{4} \text{ times} $

Work Step by Step

The variation model described by the problem is $ I=\dfrac{k}{d^2} ,$ where $I$ is the intensity of light and $d$ is the distance from the light source. Substituting $d=12$ in the equation above results to \begin{array}{l}\require{cancel} I=\dfrac{k}{12^2} \\\\ I=\dfrac{k}{144} .\end{array} Substituting $d=24$ in the equation above results to \begin{array}{l}\require{cancel} I=\dfrac{k}{24^2} \\\\ I=\dfrac{k}{576} .\end{array} Hence, when $d=24$ (doubled), the intensity of the light reduces by $ \dfrac{1}{4} \text{ times} .$
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