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About this Lesson
 Type: Video Tutorial
 Length: 4:39
 Media: Video/mp4
 Use: Watch Online & Download
 Access Period: Unrestricted
 Download: MP4 (iPod compatible)
 Size: 50 MB
 Posted: 06/27/2009
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 Exponents and Logarithms (2 lessons, $2.97)
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 UTAustin 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, padic 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
 2174 lessons
 Joined:
11/14/2008
Founded in 1997, Thinkwell has succeeded in creating "nextgeneration" 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 technologybased textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.
Thinkwell lessons feature a starstudded cast of outstanding university professors: Edward Burger (PreAlgebra through...
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I want to tell you about a realworld word problem that actually helps me in my quest to own as many automobiles as I can. There's this car I want to buy. It costs $30,000. Now, all I have right now is $27,000. Now, here's the deal. I have $27,000 right now that I can invest in a bank account that pays 6 percent interest, compounded quarterly. The question is, how long will I have to wait before I can actually buy this car, which costs $30,000?
The thing to use here is this formula that give us the future value or the amount we have in our account, after some time, given the present value, the interest rate, the number of compounding per year, with the number of years that we invest. So, just using that formula, what would we see? Well, in this case, the amount that I want at the end of the day  or, in this case, the end of the term, whenever that is is going to be $30,000. That's the future value. That equals the present value, the amount I deposit in the bank account right now, that's $27,000 times 1 plus the interest rate. Now, this is at 6 percent, so that's .06 divided by the number of compounding per year. Now, it's quarterly, so that means four per year. I raise that to the power, the number of compounding per year times the number of years.
Now, the question is how many years will I have to wait? I don't know t, but I do know m is 4. This is 4t. Why am I talking about this kind of question now, in this particular area of our discussions? Because, I want to solve for t, and notice t is in the exponent. So, what do I do? Well, I'll probably have to take logs at some point. The very first thing I would do is actually divide both sides by $27,000. So, I bring that over here, then I'll just have something with that exponent. Notice, if I bring that over, I can get rid of all those zeros. I just see a very clean . Now, if you get that 4t from an exponent and make it into a coefficient, I'll take logs of both sides. You can take any log you want  log base 10, log base e, natural log, log base 15, log base 69, I don't care. I'll take just the natural log. So, natural log on the left, I see , natural log on the right, I see , and voila. The whole value of that is that this exponent becomes a coefficient by properties of the log, and so this actually equals .
Well, I'm trying to solve for t, but now t is on the ground floor. There are no t's upstairs in the attic. I've got them all down here. In fact, everything else is a number, so I could just solve for t by dividing both sides by this, . I see that t equals  and look how easy this is  it's just this thing, . Now, that's something we can actually type into a calculator or computer, and if we do, we'd get 1.769. That's how many years I have to wait. So, I have to wait just under two years, right? It looks like one  around one and three quarters of a year, so one year, nine months. I think that's right. One year, nine months, roughly speaking, I have to wait, in order for me to be able to buy my car. ^
Exponential and Logarithmic Functions
Applying Exponents and Logarithms
Compound Interest Page [1 of 1]
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