Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 1 - Section 1.2 - Mathematical Models: A Catalog of Essential Functions. - 1.2 Exercises - Page 34: 23

Answer

$ 4 \ \mathrm{times \ brighter} $

Work Step by Step

The relation can be expressed as $ \displaystyle I = \frac{k}{d^2} $. When the chair is halfway, the distance is $ \displaystyle \frac{1}{2}d $: $$ \begin{align*} \displaystyle I &= \frac{k}{d^2} \\\\ I &= \frac{k}{\left(\frac{1}{2}d\right)^2} \\\\ I &= \frac{k}{\frac{d^2}{4}} \\\\ I &=4\left( \frac{k}{d^2} \right)\\\\ \end{align*} $$ So, the original brightness will be multiplied by $ 4$.
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