Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance

 August 30th, 2012, 11:23 AM #1 Newbie   Joined: Oct 2011 Posts: 11 Thanks: 0 Quadratics in Business Hello. So bear with me since I am a late bloomer to mathematics, but I have read that quadratics can be used to figure out financial information for a business. And as I have looked it up briefly online, I just tend to get more and more confused since many people work the problem but don't show the point a to point b. I was wondering if someone could show me how this works with an easy problem and explain why/how the pieces all fit. Please assume I know nothing since I would like to clarify what I think I know by starting at the beginning. Much thanks to anyone who is willing to take on this endeavor!
 August 30th, 2012, 07:19 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,337 Thanks: 1024 Re: Quadratics in Business [quote="Jabby J]..... but I have read that quadratics can be used to figure out financial information for a business. Read that where? Where are you at with quadratics? Can you solve 3x^2 - 13x - 10 = 0 ?
 August 31st, 2012, 04:40 AM #3 Newbie   Joined: Oct 2011 Posts: 11 Thanks: 0 Re: Quadratics in Business Well, I can get as far as 13 +- the square root of 289/6 I know 17^2 is 289 but from there I get lost. I was in a conference and as an Ice Breaker I mentioned how I like Math. The person asked if I was interested in quadratics and I said statistics specificaly (Which is true, I feel I'm decent at calculating statistical information). But when I got back to my desk at work I looked up quadratics in business in google and there were a few problems posted. I was more curious than anything. But looking into it further I thought maybe there was another corner of mathematics that might help me track paterns and data. I can see myself how calculating a graph would be helpful depending on the question/data. I just wanted to make sure I wasn't missing out I guess, and that turned into curiousity.
 August 31st, 2012, 05:27 AM #4 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Quadratics in Business Probably even more useful than quadratic polynomials are exponential equations, which have applications to stock depletion, interest, inflation, and all manner of other things.
September 6th, 2012, 04:23 AM   #5
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 Originally Posted by CRGreathouse Probably even more useful than quadratic polynomials are exponential equations, which have applications to stock depletion, interest, inflation, and all manner of other things.
I will have to look those up. Thanks for the tip.

 September 6th, 2012, 05:00 AM #6 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Quadratics in Business Basic idea: the logarithm function transforms multiplication into addition and exponentiation into multiplication, like so: log(x * y) = log(x) + log(y) log(x^y) = y * log(x) So when you have an equation where you want to solve for the exponent, you can use the logarithm to "bring it down" to solve for it. For example, if every interest period you get interest of r (say, 0.01 = 1%), you have (1 + r)^n times what you started with after n time periods, after compounding. So how long does it take you to double your money? 2 = (1 + r)^n, so log(2) = log((1 + r)^n) = n * log(1 + r) and thus n = log(2)/log(1 + r).
September 7th, 2012, 04:29 AM   #7
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 Originally Posted by CRGreathouse Basic idea: the logarithm function transforms multiplication into addition and exponentiation into multiplication, like so: log(x * y) = log(x) + log(y) log(x^y) = y * log(x) So when you have an equation where you want to solve for the exponent, you can use the logarithm to "bring it down" to solve for it. For example, if every interest period you get interest of r (say, 0.01 = 1%), you have (1 + r)^n times what you started with after n time periods, after compounding. So how long does it take you to double your money? 2 = (1 + r)^n, so log(2) = log((1 + r)^n) = n * log(1 + r) and thus n = log(2)/log(1 + r).
Thanks.. I think. Is this a similar process as using the e function? I slightly remember using the log function from high school. I guess I have way more studying to do.

 September 7th, 2012, 10:03 AM #8 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Quadratics in Business Different names for the same thing, yes: exp(x) = e^x. I chose the way I wrote about it carefully, in a way designed to introduce as little confusion as possible. When I was taught this originally it seemed very confusing because of the way it was presented.

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