Find equation for a function of form: $f(x) = Ae^{kx} \cos(Bx+C)+D.$? How can I find the equation of this function.
I assume I will need to work out coordinates for each peak?
The function is a decaying cos graph of the form:
$$f(x) = Ae^{kx} \cos(Bx+C)+D.$$
Any help would be appreciated!
 A: You plug the values into Eureqa (link here) and let it find the function for you.
I pluged the table of values from (my example)

And it found the solution

With pretty good fitting:

The original function I used in Excel was =0.8+0.8*EXP(-'t'/4)*(2*COS(PI()*'t')). 
Eureqa solution: 0.80000001 + 0.79978114*cos(-6.2831697*t)*exp(-0.25*t)
The results are impressive as you can see the 0.8 the 2*PI() and the 1/4.
A: One way is to use a multidimensional minimizer:  collect a bunch of points, create a function of $A, B, C,  D, k$ that sums the squared errors, and minimize it.  Such routines are available in any numerical analysis text, or in Excel.
To do it by eye, Eivind gave you a start.  It looks like $D$ is about $82$ (taking the center of the wiggles), $C$ is $0$ (assuming the start has a flat tangent-maybe it is $-3$ or so), $9$ waves end at $x=108$ so $B=2\pi/12$, the amplitude drops by about a factor of $4$ in $100,$ so $e^{100k}=0.25, k=-.014$ and from the first wave $A$ is about $35$.
