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Exponential help

  1. Oct 27, 2007 #1
    i don't understand this...why will y=c*a^x not fit data which has negative y-values and positive x-values?...... Will that same data fit y=c*a^x+b?

    thanks in advance
     
  2. jcsd
  3. Oct 27, 2007 #2
    Think about this: What is the domain and range of [tex]y=ca^x[/tex]? As [tex]x[/tex] increases or decreases, will the domain and range change? It helps to look at a graph of this exponential function.
     
  4. Oct 27, 2007 #3

    HallsofIvy

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    ??Actually it might. You just have to take c to be negative! Since a^x itself is always positive (whether x is negative or positive, c*a^x will be negative as long as c is negative.

    If you want to try to fit to points that have y values both positive and negative, then you will have to try something like c*a^x+ b.

    Of course, in the first case, since you have only two parameters, a and c, to determine, you can force it to fit more than two points. y= c*a^x+ b as three parameters, so you can fit that to three points.
     
  5. Oct 27, 2007 #4
    Halls makes a good point.
    Rather than analyzing the function with positive and negative values of [tex]c[/tex] and [tex]a[/tex], you can fit any two points with this function since it is in its most general form. Plus, you don't have to assume [tex]c[/tex] is restricted to be a positive number.

    Try this: Find an exponential function in the form [tex]y=ca^x[/tex] by solving for [tex]c[/tex] and [tex]a[/tex] to fit points [tex](-2,-3)[/tex] and [tex](3,2)[/tex].
     
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