Help locating a Math Equation to fit this curve

In summary, the request seeks assistance in identifying a mathematical equation that accurately represents a specific curve. The individual may provide data points or a visual representation of the curve to facilitate the fitting process, aiming to find a function that closely matches the observed pattern.
  • #1
ikihi
81
2
Rules Violation - member warned about restarting a closed thread
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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  • #2
That completely depends on the curve. Since you have not provided any more information than ”curve”, nobody can say.
 
  • #3
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.
 
  • #4
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?
 
  • #5
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:
  • #6
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.
 
  • #7
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.
 
  • #8
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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  • #9
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.
 

FAQ: Help locating a Math Equation to fit this curve

What type of data do you have, and what is the shape of the curve?

Understanding the type of data and the general shape of the curve is crucial. Whether your data is linear, quadratic, exponential, logarithmic, or another form will guide you in selecting the appropriate mathematical model. Plotting the data points on a graph can help visualize the curve and identify its characteristics.

What software or tools can I use to fit a curve to my data?

There are several software tools and programming languages available for curve fitting, including Python (with libraries like NumPy and SciPy), R, MATLAB, Excel, and specialized software like CurveExpert. Each tool has its own set of functions and methods for fitting curves to data.

How do I determine the best-fit equation for my curve?

To determine the best-fit equation, you can use methods like least squares regression, which minimizes the sum of the squares of the differences between the observed and predicted values. Many software tools offer built-in functions to perform these calculations and suggest the best-fit equation based on your data.

What are the common types of equations used for curve fitting?

Common types of equations used for curve fitting include linear equations (y = mx + b), polynomial equations (y = a + bx + cx^2 + ...), exponential equations (y = a * e^(bx)), logarithmic equations (y = a + b * log(x)), and power equations (y = a * x^b). The choice of equation depends on the nature of your data and the shape of the curve.

How can I validate the accuracy of the fitted curve?

To validate the accuracy of the fitted curve, you can use statistical measures such as the coefficient of determination (R^2), root mean square error (RMSE), and residual analysis. These metrics help assess how well the curve fits the data and whether the model is appropriate for making predictions.

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