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Math Help - Varying exponential growth

  1. #1
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    Varying exponential growth

    I have six data points and need to calculate growth along a varying growth curve. My data is:

    Year 2008 amount = 60
    Year 2009 amount = 200
    Year 2010 amount = 360
    Year 2011 amount = 570
    Year 2012 amount = 855
    Year 2013 amount = 1,195

    I know that year 2008 is made up of Q3 = 25 and Q4 = 35.

    I am trying to break the yearly amounts down to quarterly amounts. Each quarter amount must be greater than the previous quarter. Assume exponential growth from 1 year to the next.

    What would be the formula to calculate Q1, Q2, Q3, and Q4 for 2009 so that all for quarters equal 200?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mtbikerj View Post
    I have six data points and need to calculate growth along a varying growth curve. My data is:

    Year 2008 amount = 60
    Year 2009 amount = 200
    Year 2010 amount = 360
    Year 2011 amount = 570
    Year 2012 amount = 855
    Year 2013 amount = 1,195

    I know that year 2008 is made up of Q3 = 25 and Q4 = 35.

    I am trying to break the yearly amounts down to quarterly amounts. Each quarter amount must be greater than the previous quarter. Assume exponential growth from 1 year to the next.

    What would be the formula to calculate Q1, Q2, Q3, and Q4 for 2009 so that all for quarters equal 200?
    I think you need to clarify what the question is here.

    CB
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  3. #3
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    Ok. Let’s try it this way. I’m not sure I’m getting the mathematical symbols right. I am looking for an algorithm that I can apply to a set of increasing numbers that will give me the approximate slope of a non-linear but always increasing curve that will allow me to plot other coordinates along that curve.
    Here is the example above in a more mathematical format, or as close as I can come up with.
    X1=1, Y1=25
    X2=1, Y2=35
    {X3,X4,X5,X6}, Y3+Y4+Y5+Y6=200
    {X7,X8,X9,X10}, Y7+Y8+Y9+Y10=360
    {X11,X12,X13,X14}, Y11+Y12+Y13+Y14=570
    {X15,X16,X17,X18}, Y15+Y16+Y17+Y18=855
    {X19,X20,X21,X22}, Y19+Y20+Y21+Y22=1,195
    ∇(Y1,Y2,Y3…Y22), this is to say, each Yn must be greater than the previous Yn
    How can I come up with a range of numbers for say…Y17.

    All those numbers next to my variables are supposed to be in subscript.
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