Word Problem > A newscaster stated that the 1989 earthquake in southern California was a reading on the Richte

Word Problem > A newscaster stated that the 1989 earthquake in southern California was a reading on the Richter scale of 7.1, was twice as powerful as a subsequent earthquake whose reading on the Richter scale was 3.05. How much more powerful was the 7.1 earthquake than the 3.05 earthquake?

This is more of a science question - you have to know that the Richter scale is logarithmic (base 10).

The 7.1 earthquate is 10^(7.1 - 3.05) = 10^3.05 ~= 1120 times as powerful

My answer was wrong - the poster below was right that it's 11200x as powerful.

7.1 - 3.05 = 4.05

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According to the USGS "each whole number increase in magnitude represents a tenfold increase in measured amplitude; as an estimate of energy, each whole number step in the magnitude scale corresponds to the release of about 31 times more energy than the amount associated with the preceding whole number value"

Let's simplify the question a bit and use a M3.0 and and M7.0. By amplitude we see that a M4 is 10x a M3, a M5 is 100x a M3, a M6 is 1,000 a M3 and, finally a M7 is 10,000 the amplitude of a M3.

Doing the same for energy:3->4 = 31; 3->5 =961; 3->6=29791; 3->7=923521.

Shorter math would be taking the difference between the two and calling it y, then using 10^y for amplitude and 31^y for energy, thus y=7.1-3.05=4.05, so the 7.1 is 10^4.05 or 11,220x the amplitude and ~1.1 million times the energy.

Someone may want to check my math.

Twice as powerful isn't it...?