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linear and exponential graphs and x,y intercepts

  1. #1

    linear and exponential graphs and x,y intercepts

    I have two lines one linear (y=mx+c) and one exponential (y=c^bx) and
    they intercept each other. I believe it is possible to calculate where
    the lines intercept. Although I can do this by graphing the data, it
    takes time and allows for user error so a calculation would speed
    things along greatly.

    The problem:

    So for the first line using the equation y=mx+c the numbers for the
    13kPa line are y=0.0021x+9e-16

    And for the exponential line (y=c^bx) which we produce to using the
    myograph is y=0.0022^0.0046x (^=Exp)

    I know that the two lines intercept at 1613. But no matter what I try
    I can't get the equations to simplify and produce a x value.


  2. #2
    Tushar Mehta
    Guest

    Re: linear and exponential graphs and x,y intercepts

    The way to solve this is to set the 2 equations equal to one another and
    then solve for x. So, you will get
    0.0021x+9e-16 = 0.0022*EXP(0.0046x)

    For all practical purposes 9e-16 is zero. So, we get
    0.0021x = 0.0022*EXP(0.0046x)

    This cannot be solved algebriacally but it can be solved numerically.

    Designate a cell, say B2 as the one containing the X value. Then, in C2,
    enter the formula =0.0021*B2. In D2, enter the formula
    =0.0022*EXP(0.0046*B2). In E2 enter the formula =C2-D2.

    Now, use GoalSeek (Tools | Goal Seek...) to set E2 to zero by changing B2.
    Though, given the scale of the numbers, I would go with Solver (Tools |
    Solver...) Set the target as E2, set the desired value of 0 and click
    Solve.

    I get two results, both borne out by a chart. The first intersection is
    reached if you start with an initial value of 0 in B2. The second by
    starting with an initial value of 2000.

    And, for the larger result, I don't get 1631 but 1593.

    --
    Regards,

    Tushar Mehta
    www.tushar-mehta.com
    Excel, PowerPoint, and VBA add-ins, tutorials
    Custom MS Office productivity solutions

    In article <[email protected]>,
    [email protected] says...
    > I have two lines one linear (y=mx+c) and one exponential (y=c^bx) and
    > they intercept each other. I believe it is possible to calculate where
    > the lines intercept. Although I can do this by graphing the data, it
    > takes time and allows for user error so a calculation would speed
    > things along greatly.
    >
    > The problem:
    >
    > So for the first line using the equation y=mx+c the numbers for the
    > 13kPa line are y=0.0021x+9e-16
    >
    > And for the exponential line (y=c^bx) which we produce to using the
    > myograph is y=0.0022^0.0046x (^=Exp)
    >
    > I know that the two lines intercept at 1613. But no matter what I try
    > I can't get the equations to simplify and produce a x value.
    >
    >


  3. #3
    Bernard Liengme
    Guest

    Re: linear and exponential graphs and x,y intercepts

    I would suggest that y=0.0021x+9e-16 is essentially y=0.0021x (the error in
    m is greater then the value of c)
    This makes the math trivial
    best wishes
    --
    Bernard V Liengme
    www.stfx.ca/people/bliengme
    remove caps from email

    <[email protected]> wrote in message
    news:[email protected]...
    >I have two lines one linear (y=mx+c) and one exponential (y=c^bx) and
    > they intercept each other. I believe it is possible to calculate where
    > the lines intercept. Although I can do this by graphing the data, it
    > takes time and allows for user error so a calculation would speed
    > things along greatly.
    >
    > The problem:
    >
    > So for the first line using the equation y=mx+c the numbers for the
    > 13kPa line are y=0.0021x+9e-16
    >
    > And for the exponential line (y=c^bx) which we produce to using the
    > myograph is y=0.0022^0.0046x (^=Exp)
    >
    > I know that the two lines intercept at 1613. But no matter what I try
    > I can't get the equations to simplify and produce a x value.
    >




  4. #4

    Re: linear and exponential graphs and x,y intercepts

    More help needed.

    I do not have solver installed on my PC and the logistics of getting it
    put onto every PC at work is going to be impossible. So I can't use
    the solver. I do have GoalSeak if thats any help.

    Next although the y-value for this equation is near zero that will not
    be the case in all the eqautions i deal with. the equations are just
    an example.

    I want to know at what X-value do the two lines cross.

    I would preferably want it as an eqaution because I need to construct
    it using XL. Also I have done much in the way of mathematics since uni
    (about 7 years ago) so you will have to go slow. I know it's a
    terrible excuse, but I need to understand it all.

    mc+c=c^bx (^=exp).


  5. #5
    Registered User
    Join Date
    11-05-2011
    Location
    jaipur
    MS-Off Ver
    Excel 2003
    Posts
    4

    Re: linear and exponential graphs and x,y intercepts

    HI –
    I am unable to find this question on the form. I got this question during second GMAT prep exam.

    The Y intercepts of a line l is 4. If the slope of l is negative, which of the following could be the X intercept of l?
    I. -1
    II. 0
    III. 6

    (A) I only
    (B) II only
    (C) III only
    (D) I and II only
    (E) I and III only

    I really have no idea where to even begin to start solving this problem. I always have problem with lines problems.

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