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 467: 117

Answer

$188$ $decibels$; yes, it can rupture a human eardrum.

Work Step by Step

$$D(I) = 10\log(10^{12}I)$$ $$D(6.3 \times 10^{6}) = 10\log(10^{12}(6.3 \times 10^6))$$ $$D(6.3 \times 10^6) = 10\log(6.3 \times 10^18) \approx 188$$ Since the decibels produced by a blue whale are greater than 160, it can be said that a human eardrum can rupture at close range.
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