Earthquake Intensity On the Richter scale, the magnitude R of an earthquake of intensity I is given by In(I) – In(I,) R = In(10) where I, is the minimum intensity used for comparison. Assume I, = 1. (a) Find the magnitude of an earthquake with an intensity of 39,811,000. (Round your answer to one decimal place.) (b) Find the intensity of the January 23, 2015 earthquake in Vanuatu for which R = 6.8. (Round your answer to the nearest whole number.) I = (c) Find the intensity of the April 1, 2014 earthquake in Chile for which R = 8.2. (Round your answer to the nearest whole number.) I = (d) Find the factor by which the intensity is increased when the value of R is doubled. (Write the new intensity in terms of the original intensity New Intensity = dR (e) Find dI dR dI
Earthquake Intensity On the Richter scale, the magnitude R of an earthquake of intensity I is given by In(I) – In(I,) R = In(10) where I, is the minimum intensity used for comparison. Assume I, = 1. (a) Find the magnitude of an earthquake with an intensity of 39,811,000. (Round your answer to one decimal place.) (b) Find the intensity of the January 23, 2015 earthquake in Vanuatu for which R = 6.8. (Round your answer to the nearest whole number.) I = (c) Find the intensity of the April 1, 2014 earthquake in Chile for which R = 8.2. (Round your answer to the nearest whole number.) I = (d) Find the factor by which the intensity is increased when the value of R is doubled. (Write the new intensity in terms of the original intensity New Intensity = dR (e) Find dI dR dI
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Earthquake Intensity
On the Richter scale, the magnitude \( R \) of an earthquake of intensity \( I \) is given by:
\[
R = \frac{\ln(I) - \ln(I_0)}{\ln(10)}
\]
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. (Round your answer to one decimal place.)
\[
\text{Answer: } \_\_\_\_\_
\]
(b) Find the intensity of the January 23, 2015 earthquake in Vanuatu for which \( R = 6.8 \). (Round your answer to the nearest whole number.)
\[
I = \_\_\_\_\_\_
\]
(c) Find the intensity of the April 1, 2014 earthquake in Chile for which \( R = 8.2 \). (Round your answer to the nearest whole number.)
\[
I = \_\_\_\_\_\_
\]
(d) Find the factor by which the intensity is increased when the value of \( R \) is doubled. (Write the new intensity in terms of the original intensity, \( I \).)
\[
\text{New Intensity} = \_\_\_\_\_
\]
(e) Find \(\frac{dR}{dI}\).
\[
\frac{dR}{dI} = \_\_\_\_\_
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1033a793-de38-45d1-a455-c2fc05395ba1%2F987e11ad-022a-488c-8e3b-6404c2dff7bf%2F7ylzcei_processed.png&w=3840&q=75)
Transcribed Image Text:Earthquake Intensity
On the Richter scale, the magnitude \( R \) of an earthquake of intensity \( I \) is given by:
\[
R = \frac{\ln(I) - \ln(I_0)}{\ln(10)}
\]
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. (Round your answer to one decimal place.)
\[
\text{Answer: } \_\_\_\_\_
\]
(b) Find the intensity of the January 23, 2015 earthquake in Vanuatu for which \( R = 6.8 \). (Round your answer to the nearest whole number.)
\[
I = \_\_\_\_\_\_
\]
(c) Find the intensity of the April 1, 2014 earthquake in Chile for which \( R = 8.2 \). (Round your answer to the nearest whole number.)
\[
I = \_\_\_\_\_\_
\]
(d) Find the factor by which the intensity is increased when the value of \( R \) is doubled. (Write the new intensity in terms of the original intensity, \( I \).)
\[
\text{New Intensity} = \_\_\_\_\_
\]
(e) Find \(\frac{dR}{dI}\).
\[
\frac{dR}{dI} = \_\_\_\_\_
\]
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