Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.2 Mathematical Models: A Catalog of Essential Functions - 1.2 Exercises - Page 36: 29


The light is four times as bright.

Work Step by Step

By moving halfway to the lamp, $x$ is divided by $2$. Thus, by the inverse square law: $f(x) = k(\frac{x}{2})^{-2}$ $f(x) = \frac{k}{\frac{x^2}{2^2}}$ $f(x) = \frac{k}{\frac{x^2}{4}}$ $f(x) = \frac{4k}{x^2}$ Which means there is 4 times as much illumination, or the light is four times as bright.
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