In 2014, Chile experienced an intense earthquake with a magnitude of 8.2 on the Richter scale. In 2010, Haiti also experienced an intense earthquake that measured 7.0 on the Richter scale. Compare the intensities of the two earthquakes. Use a logarithmic model to solve. Round to the nearest whole number.

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:

 is equivalent to:  

8.2 = log I becomes:

So the intensity of the earthquake in Chile:

For Haiti:

R = log I

7.0 = log I

We know that:

 is equivalent to:  

7.0 = log I becomes:

So the intensity of the earthquake in Haiti:

Compare the two intensities :

=

=

= 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.

- = 8.2 - 7.0

= 1.2

Convert this logarithmic equation to an exponential equation

= 1.2

=

Hence

 = 16

The intensity of the 2014 earthquake was about 16 times the intensity of the 2010 earthquake

Step-by-step explanation:

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