College Algebra (6th Edition)

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

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.2 - Page 468: 138

Answer

Does not make sense.

Work Step by Step

See example 9 on p.463 The magnitude R of an earthquake of intensity I is given by $R=\displaystyle \log\frac{I}{I_{0}},$ where $I_{0}$ is a zero-level earthquake. For R=8, (apply $10^{(...) }$to the above formula) $\displaystyle \frac{I_{8}}{I_{0}}=10^{8}$ $I_{8}=10^{8}I_{0}$ (the intensity was $10^{8}$ of the zero-level intensity. For R=4, $I_{4}=10^{4}I_{0}.$ The ratio of the two intensities is $\displaystyle \frac{I_{8}}{I_{4}}=\frac{10^{8}I_{0}}{10^{4}I_{0}}=10^{8-4}=10^{4}$ so $I_{8}=10,000I_{4}$ The magnitude 8 earthquake has 10,000 times the intensity of the magnitude 4 earthquake (not twice, but 10,000 times as intense).
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