   Chapter 4.5, Problem 82E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Earthquake Intensity On the Richter scale, the magnitude R of an earthquake of intensity I is given by R = ln I − ln I 0 ln 10 where I 0 is the minimum intensity used for comparison.Assume I 0 =   1. (a) Find the magnitude of an earthquake with an intensity of 39,811,000.(b) Find the intensity of the January 23, 2015 earthquake in Vanuatu for which R =   6.8 .(c) Find the intensity of the April 1, 2014 earthquake in Chile for which R =   8.2 .(d) Find the factor by which the intensity is increased when the value of R is doubled.(e) Find d R / d I .

(a)

To determine

To calculate: The magnitude of an earthquake with an intensity of 39,811,000 if the magnitude of earthquake and intensity are correlated by R=lnIlnI0ln10 and it is assumed that I0=1.

Explanation

Given information:

The magnitude of earthquake and intensity are correlated by R=lnIlnI0ln10.

Calculation:

Consider an expression,

R=lnIlnI0ln10

Now substitute I0=1,

The value becomes R=lnI

(b)

To determine

To calculate: The intensity of an earthquake in Vanuatu in which magnitude of the earthquake is R=6.8 and the magnitude of earthquake and intensity are correlated by R=lnIlnI0ln10 and it is assumed that I0=1.

(c)

To determine

To calculate: The intensity of an earthquake in Chile in which magnitude of an earthquake is R=8.2 and the magnitude of earthquake and intensity is correlated by R=lnIlnI0ln10 and it is assumed that I0=1.

(d)

To determine

To calculate: The amount of intensity increased of an earthquake if the magnitude of an earthquake R is doubled and the magnitude of earthquake and intensity are approximated by the equation, R=lnIlnI0ln10 and it is assumed that I0=1.

(e)

To determine

To calculate: The value of dRdI if the amount of intensity and magnitude of an earthquake are correlated by R=lnIlnI0ln10 and it is assumed that I0=1.

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