Respuesta :
Answer:
The intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3 is about 1.3 times greater.
Step-by-step explanation:
Given : An earthquake with the magnitude 5.4 greater than an earthquake with magnitude 5.3.
To find : By what approximate factor is the intensity of an earthquake of given magnitudes is greater?
Solution :
The equation for the magnitude of an earthquake is given by
[tex]M=\log(\frac{I}{I_{0}})[/tex]
Where, I is the intensity of earthquake and [tex]I_0[/tex] is constant.
For an earthquake with magnitude 5.4,
[tex]5.4= log(\frac{I_{1} }{I_{0} })[/tex]
Similarly, for an earthquake with magnitude 5.3,
[tex]5.3= log(\frac{I_{2} }{I_{0} })[/tex]
Now, equating both the magnitudes
[tex]\frac{log(\frac{I_{1} }{I_{0} })}{log(\frac{I_{2} }{I_{0} })} =\frac{5.4 }{5.3 } \\\\(\frac{I_{1} }{I_{2} })=\frac{10^{5.4} }{10^{5.3} }\\\\(\frac{I_{1} }{I_{2} }) =10^{5.4-5.3}=1.2589\simeq 1.3\\\\I_{1} =1.3I_{2}[/tex]
The intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3 is about 1.3 times greater.
The factor is 1.3.
