Question

by what approximate factor is the intensity of an earthquake with the magnitude 5.4 greater than an earthquake with magnitude 5.3?

Answer 1

1.26 girl im going back from the test and answering all questions

Answer 2

The intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3 is about 1.3 times greater.

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

`M=\log((I)/(I_(0)))`

Where, I is the intensity of earthquake and
`I_0` is constant.

For an earthquake with magnitude 5.4,

`5.4= log((I_(1) )/(I_(0) ))`

Similarly, for an earthquake with magnitude 5.3,

`5.3= log((I_(2) )/(I_(0) ))`

Now, equating both the magnitudes

`(log((I_(1) )/(I_(0) )))/(log((I_(2) )/(I_(0) ))) =(5.4 )/(5.3 ) \\\\((I_(1) )/(I_(2) ))=(10^(5.4) )/(10^(5.3) )\\\\((I_(1) )/(I_(2) )) =10^(5.4-5.3)=1.2589\simeq 1.3\\\\I_(1) =1.3I_(2)`

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.