Results 1 to 5 of 5

Math Help - point of intersection

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    31

    point of intersection

    How the find the point of intersection of the two functions: y=300(1.05)^x and y=1000(0.92)^x? Help, Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by Hellooo View Post
    How the find the point of intersection of the two functions: y=300(1.05)^x and y=1000(0.92)^x? Help, Thanks
    I haven't looked to ensure that there exists a unique intersection point, but you can find any intersection points by solving

    300(1.05)^x = 1000(0.92)^x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Hello,
    you can let a = 1.05 and b = 0.92 to make it simpler, then you have to solve :

    300 a^x = 1000 b^x

    Taking the logarithms of base "a" yields :

    log_a(300 a^x) = log_a(1000 b^x)

    Simplifying using the log laws :

    log_a(300) + log_a(a^x) = log_a(1000) + log_a(b^x)

    Keep simplifying :

    log_a(300) + x = log_a(1000) + x log_a(b)

    Isolate the x's on one side :

    log_a(300) - log_a(1000) = x log_a(b) - x

    Simplify :

    log_a(300 / 1000) = x(log_a(b) - 1)

    Alright :

    (log_a(0.3)) / (log_a(b) - 1) = x

    Now replace a and b with the values defined at the start, do the calculation and you got x (provided it exists, you'll know it doesn't if you get a math error )

    EDIT : sorry, used 100 instead of 1000, corrected and checked against Wolfram
    Last edited by Bacterius; June 18th 2010 at 08:37 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jan 2009
    Posts
    715
      300(1.05)^x = 1000(0.92)^x

     (1.05)^x / (0.92)^x = 10/3 <br />
     (1.05/0.92) ^x = 10/3

     x log(1.05/0.92) = log(10/3)

     x = log(10/3) / log(1.05/0.92)

     = 9.109152249....
    Last edited by simplependulum; June 18th 2010 at 09:08 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2010
    Posts
    31
    Thank you very much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Point of Intersection (2)
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 5th 2010, 07:36 AM
  2. [SOLVED] Point of Intersection
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: September 4th 2010, 12:40 PM
  3. point of intersection
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: December 8th 2008, 07:37 PM
  4. Point of intersection
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 23rd 2008, 03:06 PM
  5. intersection point
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 16th 2007, 05:10 AM

Search Tags


/mathhelpforum @mathhelpforum