How to modify a power function?

[SHRock]

Homework Statement

Let's say I have 2 ordered pairs. I want to find the the a and b in the function. How would I do that?

Homework Equations

y=ax^b

The Attempt at a Solution

y/a=x^b
b=log(y/a)/logx

But now I have 2 variables. How would I find those variables?

 

[Mark44]

Homework Statement

Let's say I have 2 ordered pairs. I want to find the the a and b in the function. How would I do that?

Homework Equations

y=ax^b

The Attempt at a Solution

y/a=x^b
b=log(y/a)/logx

But now I have 2 variables. How would I find those variables?

Substitute the points you have into your equation. Then you will have two equations in the two unknowns, a and b.

 

[SHRock]

Substitute the points you have into your equation. Then you will have two equations in the two unknowns, a and b.

Yeah but the problem is I don't know how to reduce that.

Let's say I pick 2 points

(35,0.01)
(4.5,30)

so the functions will be

b=log(0.01/a)/log 35

b=log(30/a)log4.5

 

[Mark44]

Let's go back to the original equation, y = ax^b

Using your points, we have
.01 = a * 35^b
30 = a* 4.5^b

Dividing the first equation by the second, we have
.01/30 = 35^b/4.5^b = (35/4.5)^b

Can you solve that for b? Once you get b, then use either equation to find a.

 

[SHRock]

Let's go back to the original equation, y = ax^b

Using your points, we have
.01 = a * 35^b
30 = a* 4.5^b

Dividing the first equation by the second, we have
.01/30 = 35^b/4.5^b = (35/4.5)^b

Can you solve that for b? Once you get b, then use either equation to find a.

Oh ok thanks I get it. Now another little questions. Let's say if I do this for multiple ordered pairs. And a and b aren't always the same, but pretty close. Should get the average of those and plug it in as b? Because this is like a lab and error will occur.

 

[Mark44]

See if this is any help: http://en.wikipedia.org/wiki/Nonlinear_regression