Help locating a Math Equation to fit this curve

  • Context: Calculus 
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    Curve equation math
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Discussion Overview

The discussion revolves around finding a mathematical equation to fit a curve based on a set of points, specifically focusing on the relationship between concentration and values represented on the x and y axes. Participants explore various potential functions and approaches to curve fitting, while addressing the lack of information provided by the original poster (OP).

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the type of curve significantly influences the equation, noting that without more information, it is impossible to determine a fitting function.
  • One participant proposes that the curve resembles a square root function, while another later suggests it could be part of a circle, indicating the need for more data points to confirm any model.
  • There is mention of using logarithmic transformations to analyze power functions, although this is considered unreliable with only two points.
  • Several participants express concern over the insufficient information provided by the OP, emphasizing the need for specific ordered pairs and units for the axes to make meaningful contributions.
  • Exponential decay is introduced as a possible function due to the context of concentration, but again, the lack of data points is highlighted as a critical limitation.

Areas of Agreement / Disagreement

Participants generally agree that there is insufficient information to arrive at a definitive equation or model. Multiple competing views on potential functions exist, but no consensus is reached regarding the best approach.

Contextual Notes

Limitations include the absence of specific data points, unclear definitions of the axes, and the lack of additional context that could inform the choice of mathematical models.

ikihi
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The concentration is the Y axis, and the values are the x axis. What is the equation for finding a target value on a curve between set of points?
curve.png
 
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That completely depends on the curve. Since you have not provided any more information than ”curve”, nobody can say.
 
ikihi said:
The concentration is the Y axis, and the values are the x axis. What is the equation for finding a target value on a curve between set of points?
That looks a bit like a square root function.
Swap the x and y axes, and it becomes a parabola.
It takes three known points to fit a parabola, but you only have two.
The best you can do with two points is a straight line.

Log-Log graphs are good for power functions. Maybe if you plot Log(x) against Log(y) to get a straight line, it would make interpolation easier, but still unreliable. That assumes there is no data less than or equal to zero on the x or y axis.
 
ikihi said:
The concentration is the Y axis, and the values are the x axis. What is the equation for finding a target value on a curve between set of points?
View attachment 335714
I have not read other responses yet and have not picked at this one yet, but the curve drawn appears like part of a circle. Can you work that way with your example?

Also, the description for your graph is incomplete. WHAT is the x-axis? What are those "values" supposed to mean?
 
ikihi
We cannot be sure what points we see accented on your graph. What are the ordered pair of those points accented in the big red dots?

edit: If we try to estimate to read your two points they may be (6.9 , 0.0093) and (4.8, 0.0041) .

If we guess that you have attempted to fit your scale numberings to the points, as off as they appear, these might be (4.8, 0.0040) and (7.0, 0.0080).
What ARE the two given points?
 
Last edited:
I changed my mind. I do not like the idea of fitting those only two points to a circle. Better for some square root function or logarithmic function. Still we no know your actual given points.
 
To be honest, neither the square root function norbthe circle seem like good firs to me. This entire discussion just accentuates what I already said in #2. There is way too little information in the OP to make anything but guesswork.
 
Orodruin said:
There is way too little information in the OP to make anything but guesswork.
Concentration suggests chemistry, which suggests adding exponential decay to the list of possible functions.

Like a good mystery, we need a couple of more data points, and units for the axes.
 
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Baluncore said:
Concentration suggests chemistry, which suggests adding exponential decay to the list of possible functions.

Like a good mystery, we need a couple of more data points, and units for the axes.
Did you also note the scales of the x and y axes? My point is not that it is a good mystery, my point is that it the mystery is not well defined, making any speculation meaningless.
 
  • #10
Orodruin said:
Did you also note the scales of the x and y axes? My point is not that it is a good mystery, my point is that it the mystery is not well defined, making any speculation meaningless.
That's right. And we have not been informed better since @ikihi posted.
 
  • #11
Thread closed.
The OP started this thread after an earlier thread was deleted by another mentor. Homework and homework-type questions must be posted in the relevant subforum of the Homework Help section.
 

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