Getting Power Function given points.

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SUMMARY

The discussion focuses on deriving a power function from a set of four points representing (x, y) values, which appear to describe a decaying function. Participants suggest fitting various polynomial degrees (1 to 4) or considering alternative functional forms such as exponential functions. The recommended approach is to select a functional form, specifically the power function y = ab^x, and use two of the provided points to create equations for solving the constants a and b.

PREREQUISITES
  • Understanding of polynomial fitting techniques
  • Knowledge of exponential functions and their properties
  • Familiarity with solving systems of equations
  • Basic grasp of data modeling concepts
NEXT STEPS
  • Research polynomial regression techniques for data fitting
  • Learn about exponential decay functions and their applications
  • Explore methods for solving systems of equations in two variables
  • Investigate curve fitting tools in software like Python's NumPy or SciPy
USEFUL FOR

Students in mathematics or statistics, data analysts, and anyone interested in modeling data with power or exponential functions.

krnhseya
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Homework Statement



I have 4 points (x and y values) and I was wondering how I can make an equation out of it.
It looks like a decaying function.

Homework Equations



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The Attempt at a Solution



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I absolutely have no idea how to approach this...Sorry.
 
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That's quite an open-ended problem you've got there. You could fit polynomials of degrees 1, 2, 3, or 4 to your data set. And who says it has to be a polynomial? Why not an exponential? My advice would be to pick some functional form, and then try to make a best fit.
 
Since you refer to a "power function" and "decaying function" I would guess that you are looking for a function of the for y= abx. Two values of (x,y) will give two equations to solve for a and b.
 

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