Question

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.

Answer 1

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

Explanation:

Answer 2

The intensity of the earthquake in Chile was about 16 times the intensity of the earthquake in Haiti.

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:

`y = log a_(x)` is equivalent to:
`x = a^(y)`

`R = log I`

8.2 = log I becomes:

`I = 10^(8.2)`

So the intensity of the earthquake in Chile:

`I_(Chile) = 10^(8.2)`

For Haiti:

R = log I

7.0 = log I

We know that:

`y = log a_(x)` is equivalent to:
`x = a^(y)`

`R = log I`

7.0 = log I becomes:

`I = 10^(7.0)`

So the intensity of the earthquake in Haiti:

`I_(Haiti) = 10^(7)`

Compare the two intensities :

`(I_(Chile) )/(I_(Haiti) ) }`

`= (10^(8.2) )/(10^(7) )`

=
`10^(8.2-7.0)`

=
`10^(1.2)`

= 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.
`(I_(Chile) )/(I_(Haiti) ) }`

`log I_(Chile)` -
`log I_(Haiti)` = 8.2 - 7.0

`log((I_(Chile) )/(I_(Haiti) ) })` = 1.2

Convert this logarithmic equation to an exponential equation

`log((I_(Chile) )/(I_(Haiti) ) })` = 1.2

`10^(1.2)` =
`(I_(Chile) )/(I_(Haiti) ) }`

Hence

`(I_(Chile) )/(I_(Haiti) ) }` = 16