   Chapter 11.1, Problem 51E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Richter scale The Richter scale reading, R, used for measuring the magnitude of an earthquake with intensity I is determined by R = ln ( I / I 0 ) ln  10 where I 0 is a standard minimum threshold of intensity. If I 0 = 1 , what is the rate of change of the Richter scale reading with respect to intensity?

To determine

To calculate: The rate of change of Richter scale reading with respect to the intensity, when magnitude of the earthquake with intensity I is,

R=ln(II0)ln10.

Explanation

Given Information:

The Richter scale reading R, used for measuring the magnitude of the earthquake with intensity I is determined by,

R=ln(II0)ln10

Where, I0 is a standard minimum threshold of intensity.

Formula Used:

The derivative logarithmic function:

ddx(lnx)=1x

The logarithmic identity:

ln(uv)=lnulnv

Calculation:

Consider the provided function R=ln(II0)ln10

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