Getting Power Function given points.

In summary, the conversation is about creating an equation from 4 given points with x and y values, with the assumption that it is a decaying function. Suggestions are made to try fitting polynomials or an exponential to the data set in order to find the best fit. The possibility of using a power function is also mentioned, with the suggestion to solve for the unknown variables using two of the given points.
  • #1
krnhseya
103
0

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



n/a

The Attempt at a Solution



n/a

I absolutely have no idea how to approach this...Sorry.
 
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  • #2
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.
 
  • #3
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.
 

1. What is a power function?

A power function is a mathematical function of the form f(x) = axn where a is a constant and n is a real number. It is characterized by its ability to model exponential growth or decay.

2. How do I find a power function given a set of points?

To find a power function given a set of points, you will need to use the general form of a power function and solve for the values of a and n using the given points. This can be done by setting up a system of equations and solving for the unknown variables.

3. Can any set of points be represented by a power function?

No, not all sets of points can be represented by a power function. Power functions have specific characteristics and can only model certain types of relationships between variables. In some cases, a different type of function may be more appropriate for the given points.

4. What is the importance of finding a power function for a set of points?

Finding a power function for a set of points allows us to understand the relationship between the variables and make predictions or calculations based on the model. It also helps to simplify complex data and make it easier to analyze.

5. Are there any limitations to using a power function to model data?

Yes, there are limitations to using a power function to model data. Power functions are best suited for data that exhibits exponential growth or decay, and may not accurately represent data that follows a different pattern. It is important to consider the context and nature of the data before using a power function as a model.

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