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College Algebra: The Richter Scale

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About this Lesson

  • Type: Video Tutorial
  • Length: 3:22
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 36 MB
  • Posted: 06/26/2009

This lesson is part of the following series:

College Algebra: Full Course (258 lessons, $198.00)
Algebra: Exponential and Logarithmic Functions (36 lessons, $49.50)
College Algebra: Applying Logarithmic Functions (2 lessons, $1.98)

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found athttp://www.thinkwell.com/student/product/collegealgebra. The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

About this Author

Thinkwell
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Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

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So now I want to take a look at some word problems that actually involve logarithms. That's right, it's time once again for solving real world problems. But this time, using logs. Okay, so now the first thing I want to tell you about... Oh, my God! It's an earthquake! Get under your tables! I hope everyone's okay. Look at the set. My God! Play-doh. Everything was falling. Hope you're okay. I wonder what kind of earthquake--that was a serous earthquake, it really was, and I wonder what the intensity was. You can measure that on the Richter Scale. Now, I can make a phone call here and try... I'm going to find out what the intensity of that was, because that was something, I tell you. Yes, what was the intensity of the earthquake we just felt? No, we did have an earthquake. Well, we had one here in the studio. Yeah, what was it? Okay, okay, okay. It was an intensity of--wow! 398,107,000 I[0]. Okay. Thanks very much.
I'm still a little shaken by that. But it turns out that actually, if you want to figure out on the Richter Scale what an earthquake actually showed up at, you can figure that out using logarithms, because here's the formula for it. The Richter Scale is actually a logarithmic scale, and it's just log of I, the intensity, divided by I[0]. And I[0] is the measure of a zero-level earthquake, sort of a standardizing thing. So, in fact, when you actually measure the intensity of an earthquake, it's always in terms of I[0]^. Okay, even though I'm shaken, let's see if we can actually now figure out what the Richter Scale measure we would have for the earthquake we just had. Well, all I've got to do is sort of plug in to this formula. So r = the log, and that means log[10] I/ I[0] so the Richter Scale for this one would be log of, well, on the top I'd have 398,107,000 I[0 ]divided by I[0]. By the way I[0]^ is sometimes referred to as "I-naught."
Well, these cancel and so I just see the log of 398,107,000. SO that actually is what this earthquake would have shown up on the Richter Scale. Let me see if I can actually compute that for you. I don't know, that might be too big of a number. We'll give it a shot. 398,107,123. 8.599 on the Richter Scale. That is--now you understand why I was so scared. I computed that on the calculator and I see that this earthquake registered an 8.599 on the Richter Scale. The Richter Scale is a logarithmic scale that requires logs. Now you can actually figure out exactly how fast or how awful or how serious an earthquake was.
Well, I'm going to collect myself, collect my thoughts. We'll come back and try some more word problems up next.
Exponential and Logarithmic Functions
Applying Logarithmic Functions
The Richter Scale Page [1 of 1]

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