Creating an equation and isolating a variable.

[iceisnice]

Hello everybody!

I am a young guy with an interest in mathematics and other stuff. I like to ponder on things.

Here's what I was up to. Lets say I have sets of data. I have them in excel and I plot them. The trendline is power type and it follows the data points pretty nicely, eg R around 0.9. There is some sort of an equation that estimates these trendlines. The equation depends of constant Z, which I can measure and changing Z makes a new trendline. I can measure a few sample of the data on x and y axis, and the contant Z, so I can plot them and draw a trendline. How could I make up some sort of a formula so that I could predict the new trendline for a value of constant Z I have not measured, following the existing pattern of how they change in response to that constant.

So basically I want a trend of trendlines, how they tend to change when Z changes. Is this possible to do in Excel or some other software, is it possible at all?

Another problem I am having is isolating variable n from this formula:

a=bn(1+Cn^2)^0,5

I get it down to:

n^2+Cn^4=a/b

I can't think of a way to get rid of the C. Is it even possible to isolate a variable from all formulas?

 

[Denis]

n^2+Cn^4=a/b
I can't think of a way to get rid of the C. Is it even possible to isolate a variable from all formulas?

Cn^4 + n^2 - a/b = 0 : that's a quadratic
Let x = n^2; then:
Cx^2 + x - a/b = 0
Solve for x; then n : GOT IT??

 

[Denis]

a=bn(1+Cn^2)^0,5
I get it down to:
n^2+Cn^4=a/b

Not quite...
a = bnSQRT(1+Cn^2)
a^2 = b^2 n^2 (1 + Cn^2)
a^2 / b^2 = n^2 + Cn^4
and then:
Cn^4 + n^2 - a^2 / b^2 = 0

 

[iceisnice]

Thank you, didn't see it as a quadratic before, heh.