Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - Chapter Review - Chapter Test - Page 348: 23

Answer

(a) $83\ dB$ (b) $31623$

Work Step by Step

(a) Given $D=80\ dB$, we have $80=10log\frac{I}{I_0}\longrightarrow \frac{I}{I_0}=10^8$. When the intensity is $2I$, we have $D=10log\frac{2I}{I_0}=10log(2\cdot10^8)=80+10log2\approx83\ dB$ (b) Assume we need $x$ number of people, we have $125=10log\frac{xI}{I_0}=10log10^8x=80+10logx$, thus $logx=4.5$ and $x=10^{4.5}\approx31623$
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