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mixer [17]
3 years ago
11

In 2014, Chile experienced an intense earthquake with a magnitude of 8.2 on the Richter scale. In 2010, Haiti also experienced a

n 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.
Mathematics
1 answer:
serg [7]3 years ago
6 0

Answer:

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:

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 :

\frac{I_{Chile} }{I_{Haiti} } }

= \frac{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. \frac{I_{Chile} }{I_{Haiti} } }

log I_{Chile} - log I_{Haiti} = 8.2 - 7.0

log(\frac{I_{Chile} }{I_{Haiti} } }) = 1.2

Convert this logarithmic equation to an exponential equation

log(\frac{I_{Chile} }{I_{Haiti} } }) = 1.2

10^{1.2} = \frac{I_{Chile} }{I_{Haiti} } }

Hence

\frac{I_{Chile} }{I_{Haiti} } }  = 16

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