# How to create function that is a power law

If I have a starting and ending y value and know the range along the x-axis, how can I create a function that adheres to a power-law?

Ex: I want the function to start at (1, 10), end at (1000,0). Can one creata a simple power law function given two points as such?

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## 1 Answer

well, power law functions look like $y=ax^k+b$ that's three variables ($a,k,b$) and you didn't specify any of them. But, you specified $y=0$ , which leads to $b=-a\times1000^k$ and also $10 = a-a\times1000^k$, $$\log_{1000}(1-{10\over a}) = k$$

So you can pick any $a > 10$, $b = 10 - a$ and see $k$ above.

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