Two unknown variables in experiment equation

[smashyash]

Homework Statement

I'm given an experimental equation:

y = sqrt[A^2*exp(x/d)]

(with a linear trend of ln(y^2) versus x)

I am suppose to determine the values of first A, then d given a linear fit slope and a y intercept.

Homework Equations

y = mx + b

The Attempt at a Solution

At first, I simply took the y intercept value and plugged that into y and plugged 0 in for x. I thought this would give me A since no matter what the value of d at that point, the exp will be exp(0) = 1. But this is not the case and I'm not sure how to use the given slope. Should I try setting the y = mx + b equal to the equation and solve for the variables??

 

[I like Serena]

The linear trend means:

ln(y^2) = mx + b

Btw, what would ln(y^2) evaluate to?

 

[smashyash]

I'm really not sure...

I don't really see how ln(y^2) relates to the equation, there's no way to manipulate the equation to get just that on one side..

 

[ideasrule]

You know y = sqrt[A^2*exp(x/d)], so what is y^2? How about ln(y^2)?

BTW it's useful to know that ln(a*b)=ln a + ln b

 

[smashyash]

Ok, so here's the algebra I have:

y^2 = A^2*exp(x/d)

ln(y^2) = ln( A^2 * exp(x/d) )

ln(y^2) = ln(A^2) + x/d

So if this is true, then is ln(A^2) = b and 1/d = m?
y = mx + b

 

[ideasrule]

Yes, that's exactly right. You're supposed to determine the values of A and d, though, so just invert the equations you already have.

 

[smashyash]

great! thanks so much! :)