Have exponential graph, find equation?

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  • Thread starter Thread starter ww2steel
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    Exponential Graph
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Discussion Overview

The discussion revolves around finding an equation for a set of exponential graphs based on given points. Participants explore methods for fitting equations to multiple data points, including the challenges posed by additional constraints such as a point approaching infinity at a specific angle.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • Mike presents a set of points and suggests an approximate equation, seeking a more efficient method to derive equations for numerous datasets using Excel.
  • Mike mentions a fourth point at infinity at 90 degrees, expressing confusion about how to incorporate this into his existing equations.
  • One participant proposes using a secant function variant to accommodate the point approaching infinity, suggesting a general form for the equation.
  • Another participant recommends using Excel's trendline feature or a least squares regression approach to fit a power series to the data points, providing a specific logarithmic relationship as a potential model.

Areas of Agreement / Disagreement

Participants present various methods and models for fitting equations to the data points, but there is no consensus on the best approach or the correct form of the equation. Multiple competing views remain regarding how to handle the additional point at infinity.

Contextual Notes

The discussion includes assumptions about the nature of the data and the mathematical models being used, with some participants suggesting specific forms without resolving the implications of the infinity constraint.

ww2steel
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Hi, It's been so long since I took any math classes! Please bear with me. I have sets of three points on various exponential graphs such as 0=100, 30=138, and 60=392 (x and y). I have found manually that this equation is somewhere very close to y=.0025x^2.85+100. I CAN do these manually (plugging in numbers into Excel and modifying them to hit the desired points on a graph), but I have a few HUNDRED of these sets. Is there a faster way? Hopefully that I can put in the 0, 30, and 60 values and Excel can determine the equation? (The built in Excel equations I have used from the graphs so far are completely wrong for what I am doing.)

Please shoot me an email if you can help me! It will help me so much! (Please keep it simple!)

Thanks a lot!
Mike
 
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The graph

In case it helps to figure out what my non-technical post is talking about. I need to put a line through all three pink dots. The pink dots move all around, but they are all reachable with variations of the above equation. Please help me find an easier way to do this. (Upon reevaluation I have over a thousand of these to do!) Thanks!
 

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Infinity at 90°!

Ah, crap, I just realized I have a fourth point - infinity at 90 (degrees). Do I need to throw a cosine in there or something, now I'm fairly lost. My current equations do not go to infinity at any set point, (limit?), nor do I know how to make them do so.

Please help?
 

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Last edited:
infinity at ninety degrees means your function is probably some variant of secant(x). Just try a*secant(x) + b, or maybe a*secant(x)2+b*secant(x)+c for a,b,c unknown constants. That way you're guaranteed to be able to solve for them algebraically, but the picture may not be what you're looking for
 
Last edited:
I Excel you should be able to fit a power series trendline (on the graph). Right-click on any point of the series, then click "Add trendline." Then choose type.

An alternative is to run a least squares regression using Excel's Data Analysis Toolpak Add-In. (You may have to install Data Analysis TPAI first.)

The easiest linear equation to estimate would be Log[y-100] = a + b Log[x].

y = 100 + c*x^b ===> Log[y-100] = Log[c] + b Log[x] = a + b Log[x], where a = Log[c].
 

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