Respuesta :
Answer:
The intensity of the earthquake in Chile was about 16 times the intensity of the earthquake in Haiti.
Step-by-step explanation:
Given:
magnitude of earthquake in Chile = 8.2
magnitude of earthquake in Haiti = 7.0
To find:
Compare the intensities of the two earthquakes
Solution:
The magnitude R of earthquake is measured by R = log I
R is basically the magnitude on Richter scale
I is the intensity of shock wave
For Chile:
given magnitude R of earthquake in Chile = 8.2
R = log I
8.2 = log I
We know that:
[tex]y = log a_{x}[/tex] is equivalent to: [tex]x = a^{y}[/tex]
[tex]R = log I[/tex]
8.2 = log I becomes:
[tex]I = 10^{8.2}[/tex]
So the intensity of the earthquake in Chile:
[tex]I_{Chile} = 10^{8.2}[/tex]
For Haiti:
R = log I
7.0 = log I
We know that:
[tex]y = log a_{x}[/tex] is equivalent to: [tex]x = a^{y}[/tex]
[tex]R = log I[/tex]
7.0 = log I becomes:
[tex]I = 10^{7.0}[/tex]
So the intensity of the earthquake in Haiti:
[tex]I_{Haiti} = 10^{7}[/tex]
Compare the two intensities :
[tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]
[tex]= \frac{10^{8.2} }{10^{7} }[/tex]
= [tex]10^{8.2-7.0}[/tex]
= [tex]10^{1.2}[/tex]
= 15.848932
Round to the nearest whole number:
16
Hence former earthquake was 16 times as intense as the latter earthquake.
Another way to compare intensities:
Find the ratio of the intensities i.e. [tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]
[tex]log I_{Chile}[/tex] - [tex]log I_{Haiti}[/tex] = 8.2 - 7.0
[tex]log(\frac{I_{Chile} }{I_{Haiti} } })[/tex] = 1.2
Convert this logarithmic equation to an exponential equation
[tex]log(\frac{I_{Chile} }{I_{Haiti} } })[/tex] = 1.2
[tex]10^{1.2}[/tex] = [tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]
Hence
[tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex] = 16
Answer:
The intensity of the 2014 earthquake was about 16 times the intensity of the 2010 earthquake
Step-by-step explanation:
