The Richter scale defines the magnitude of an earthquake, M,...

The Richter scale defines the magnitude of an earthquake, $M$, by the energy it releases, $E$ (measured in joules) according to $M=(-4.4+\log E) / 1.5$. (a) Find the energy released by the 1906 San Francisco earthquake, which registered $M=8.2$ on the Richter scale and devastated the city. (b) The Boxing Day Tsunami of 2004 was caused by an earthquake in the Indian Ocean that registered $M=9.1$ on the Richter scale. Find the energy released by this earthquake. (c) If the energy of one earthquake is 10 times that of another, how much greater is its magnitude on the Richter scale?

Transcript

0:00 Hello.

00:02 Okay, they give us the formula that the magnitude of an earthquake on the richter scale is equal to negative 4 .4 plus the log of the energy that is released, which is something that they have to estimate.

00:21 And then that value is divided by 1 .5.

00:25 So the first question is to find the energy for an earthquake with 8 .2.

00:32 So if we put a plug 8 .2 in for the magnitude.

00:38 Now the only thing we don't know is e, and we can just solve for e.

00:41 We're going to multiply both sides by 1 .5, plus log of e, divided by 1 .5.

00:52 If we multiply both sides by 1 .5, we get 12 .3, and then we have negative 4 .4 plus the log of e.

01:05 And then we add 4 .4 to both sides, and we get 16 .7 is equal to the log of e.

01:17 And remember that the log, when there is not a base listed, is log base 10 of e.

01:22 So if i take 10 to the power on both sides, 10 to the power of the log of e goes away, and 10 to the power of 16 .7 gives me a value of e is equal to 5 .0119 times 10 to the 16th power, joules, or a whole lot.

01:56 10 to the 16th power means we have a 17 -digit number.

01:59 So that's hundreds, thousands, millions, billions, trillions would be 15.

02:08 So it would be 50 trillion joules of energy.

02:14 So that was the first question, or the first part of that question.

02:19 The second part is to do the same thing, to plug in to the same formula.

02:24 But now we're plugging in for a stronger richter scale of 9 .1 is equal to negative 4 .4 plus the log of e all divided by 1 .5...

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