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On the Richter Scale, the magnitude R of an earthquake of intensityI is
R = log10 I/Io
where lo is a reference intensity. At 7:23am on March 19, 2003, an earthquake measuring 3.0 on the Richter scale occurred near the town of Nephi. An earthquake of that magnitude is often felt, but rarely causes damage. By comparison, the earthquake that struck San Francisco in 1906 measured 8.25 on the Richter scale. It was ___________times as intensive as the Nephi earthquake.

Respuesta :

pedrocarratore

Answer:

177,827.941

Step-by-step explanation:

The magnitude of an earthquake is given by:

[tex]R=log(\frac{l}{l_0})[/tex]

The intensity of the Nephi earthquake is:

[tex]3.0=log(\frac{l_N}{l_0})\\10^3 =\frac{l}{l_0} \\l_N=1,000*l_0[/tex]

The intensity of the San Francisco earthquake is

[tex]8.25=log(\frac{l_S}{l_0})\\10^{8.25} =\frac{l_S}{l_0} \\l_S=177,827,941*l_0[/tex]

The intensity ratio is:

[tex]r= \frac{l_S}{l_N}=\frac{177,827,941*l_0}{1,000*l_0}\\r= 177,827.941[/tex]

The San Francisco earthquake was 177,827.941 times as intensive as the Nephi earthquake.

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