Finding a Power Function for a Set of Data: Techniques and Tips

In summary, the conversation discusses the difficulty in finding a power function for a set of data and various techniques for deriving it. The suggestion of using logarithms and the least squares method are mentioned, but the person is unable to use technology for this task and is looking for alternative ideas. They also mention using a computer for a more accurate curve and ask for more data if needed.
  • #1
lalala_land89
7
0
Modeling with power functions.

I have turned to every book i own on math from algebra to math encyclopedia to calculus ab book. I seriously don't know how to come up with a power function for a set of data. I don't even know any techniques. There are no zeros or intercepts to this set of data.if anyone could please help me come with this function. i don't even know where to start or how.
x y
32 6
48 14
64 24
80 38
96 55
112 75
OK may be I am stupid but I'm in calc and yes i don't know how to come with a function. so please help.
marina
 
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  • #2
[tex]y=(1.9\cdot 10^{-5})x^3 + 0.004x^2 + 0.052x - 0.0622[/tex]
[tex]y = (1.1\cdot 10^{-7})x^4 + (2.2\cdot10^-5)x^3 + 0.0019x^2 + 0.208x - 3.28[/tex]
They both fit pretty well, but the 2nd one fits better i think.

You know how to find the derivative at a point yes? Look up Taylor series on wikipedia and on this forum, it'll help alot. FYI i didnt get that approximation through that Method, I used my computer. More data points will get a more accurate curve, post more data if you want.
 
Last edited:
  • #3
The usual way to fit a power function y = Ax^b is to take logs and fit the straight line (log y) = (log A) + b (log x)

A search for "Least squares method" should find more details.
 
  • #4
i can't use technology for this i have to derive it myself.
 
  • #5
im not aware of that method i'll try it. does anyone else have any ideas?
 
  • #6
Please don't post the same question multiple times.
 
  • #7
i didnt post twice. i posted in math forum first not realizing there's a homework forum. I'm new here. i don't quiete get the method you told me about. anymore ideas?
 

1. What is a power function and how is it used in modeling?

A power function is a mathematical equation of the form f(x) = axn, where a is a constant and n is a power. In modeling, power functions are used to describe relationships between two variables, where one variable is raised to a certain power. They are commonly used in fields such as physics, economics, and biology to represent real-world phenomena.

2. What are the key features of a power function?

The key features of a power function include the constant term (a), the power term (n), and the variable (x). The value of the constant term determines the y-intercept of the graph, the power term determines the shape of the curve, and the variable represents the input value.

3. How do you determine the domain and range of a power function?

The domain of a power function is all the possible input values (x) that can be plugged into the equation. Since the power function is defined for all real numbers, the domain is (-∞, ∞). The range of a power function depends on the value of the power term (n). If n is even, the range is (0, ∞). If n is odd, the range is (-∞, ∞).

4. How do you graph a power function?

To graph a power function, you can plot a few points and then connect them with a smooth curve. The number of points you need to plot depends on the value of the power term (n). If n is even, you need at least two points on each side of the y-axis. If n is odd, you need at least one point on each side of the y-axis. You can also use a graphing calculator or online graphing tool to quickly graph a power function.

5. What are some real-world applications of power functions?

Power functions have many real-world applications, such as modeling population growth, financial investments, and projectile motion. They can also be used to describe the relationship between electricity and resistance, as well as the spread of diseases. In economics, power functions can be used to model the relationship between price and demand or between production and cost.

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