Chapter 6.2, Problem 64E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Noise Level With the installation of noise suppression materials, the noise level in an auditorium was reduced from 93 to 80 decibels. Use the function in Exercise 63 to find the percent decrease in the intensity level of the noise as a result of the installation of these materials.

To determine

To calculate: The decrease in percent in the intensity level of the noise as a result of the installation of noise suppression materials.

Explanation

Given:

By the installation of noise suppression materials in the auditorium, the noise level was reduced from 93 to 80 decibels.

Formula used:

logab=bloga

iflogax=bthen,x=ab

Calculation:

Let us consider the expression, Î²(I)=10log10II0

By putting Î²(I)=93 and I0=10âˆ’16 in above equation, we get

Î²(I)=10log10I1I093=10log10I110âˆ’169.3=log10I1âˆ’log1010âˆ’16=log10I1+16

By further simplifying,

âˆ’6.7=log10I1I1=10âˆ’6

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