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

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

$M=\log(\frac{I}{I_{0}})$

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

For an earthquake with magnitude 5.4,

$5.4= log(\frac{I_{1} }{I_{0} })$

Similarly, for an earthquake with magnitude 5.3,

$5.3= log(\frac{I_{2} }{I_{0} })$

Now, equating both the magnitudes

$\frac{log(\frac{I_{1} }{I_{0} })}{log(\frac{I_{2} }{I_{0} })} =\frac{5.4 }{5.3 } \\\\(\frac{I_{1} }{I_{2} })=\frac{10^{5.4} }{10^{5.3} }\\\\(\frac{I_{1} }{I_{2} }) =10^{5.4-5.3}=1.2589\simeq 1.3\\\\I_{1} =1.3I_{2}$

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.