College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Summary, Review, and Test - Review Exercises - Page 438: 80


Loudness = $112$ $decibels$

Work Step by Step

Since loudness varies INVERSELY with the square of the distance from the speaker, we can express this in the following manner: $$ld^{2} = k$$ where $l$ is the loudness of the stereo speaker, $d^{2}$ is the square of the distance from the speaker and $k$ is a proportionality constant. Since we know that, when $d=8$, $l=28$, we can find $k$: $$k=ld^{2} = (28)(8^{2}) = (28)(64) = 1792$$ and finally answer the question: $$l = \frac{1,792}{4^{2}} = \frac{1,792}{16} = 112$$
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