Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.7 Applications of Exponential Functions and Logarithmic Functions - 12.7 Exercise Set - Page 834: 17

Answer

The loudness of this sound level is 130 decibels.

Work Step by Step

The intensity of sound from the race car is about $10\text{ W/}{{\text{m}}^{\text{2}}}$. Thus, $I=10$. Substitute $I=10$ and ${{I}_{0}}={{10}^{-12}}$ in the formula $L=10\cdot \log \frac{I}{{{I}_{\left( 0 \right)}}}$ and solve as follows: $\begin{align} & L=10\cdot \log \frac{I}{{{I}_{\left( 0 \right)}}} \\ & L=10\cdot \log \frac{10}{{{10}^{-12}}} \\ & L=10\cdot \log {{10}^{13}} \\ \end{align}$ Now convert it into an exponential equation by using the formula ${{\log }_{a}}x=m\rightarrow{{a}^{m}}=x$: $\begin{align} & L=10\cdot \log {{10}^{13}} \\ & L=10\cdot 13\log 10 \\ \end{align}$ $\begin{align} & L=10\cdot 13\log 10 \\ & L=10\cdot 13\cdot 1 \\ & L=130 \\ \end{align}$
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