Hi,

The question, as I understood from the OP's posting, is not how to obtain
f(x) and g(x) for two sets of real-life data; the OP says "I can get the
curve formulas by graphing them and requesting the trendline feature,...".
(Incidentally, the functions have got to be one of the types that the
Trendline tool can handle, which are linear, exponential, logarithmic,
polynomial, ...). The OP's question, on the other hand, was how to find the
intersection point of f(x) and g(x).

As I did mention in my earlier response, I do agree that Solver can
certainly find the intersection point. However, my point is, if the solution
for x when f(x)=g(x) can be expressed as an explicit analytical function
(which is possible if both functions are linear, quadratic, simple
exponential, logarithmic, or power functions, and not higher order
polynomials), calculating the intersection point using such an analytical
solution is certainly superior to finding an 'optimized' solution using
Solver. Any optimization method, including Solver, is limited by the
optimization criteria (algarithm used, convergence criterion, decimal
tolerance, .....), and also on the initial values of the optimization
parameters (in this case x-value of the intersection point). Of course, for
simple functions such as the ones considered here, the Solver-result may be
as good as the analytical solution, but the analytical solution is absolute.
An added advantage with analytical solutions, as I had mentioned, is that the
solutions update when the functions change (As you correctly pointed out, the
same can be accomplished by using Calculate Event Handler to run Solver).

A couple of questions about your remarks. My apologies if I haven't
understood those remarks correctly.

"If the OP's functions are simple low order polynomials, logarithmic or
exponential functions to begin with, it'd be inefficient for the OP to be
fitting trend lines." But, aren't those the only function-types that
Trendline handles (besides moving-averages)? What type of functions would
lend themselves to be efficient to be fit with trendlines? And, when the
functions do belong to those simple types, how would you efficiently fit them
to real data without using Trendline (or Solver for that matter)?

"And the trend lines aren't necessarily good approximations for the
underlying functions near the point of intersection. Solver is ........
likely to be more accurate than finding the intersection point of trend line
approximations to the underlying functions."
f(x) and g(x) are two functions that happen to intersect at some x,y-point
when somebody plots them out on a common graph; crudely put, the functions
don't even know the existence of each other (If the two functions are
coupled/correlated it is a totally different story). Any uncertainty in
finding the intersection point of f(x) and g(x) depends on the quality of how
well each function fits its respective x,y-data and how those uncertainties
add up near the intersection point. Calculating the intersection point using
the analytical solution can not diminish the inherent uncertainty in the
intersection point, but it would certainly not worsen it; on the other hand,
an optimaztion method such as Solver could, in certain situations, add some
extra uncertainty to the solution due to inherent limitations of the method.
But then, when explicit analytical solutions are not possible for a sytem of
equations, one has to resort to optimization methods.

Regards,
B. R. Ramachandran


"Harlan Grove" wrote:

"B. R.Ramachandran" wrote...
....
My purpose of asking the OP for the functional forms of f(x) and g(x)
was that, if both are linear, logarithmic, simple exponential, quadratic,
or
power functions (and not higher order polynomials), then the x-value (and
from it, the y-value) of the intersection point can be obtained using
analytical formulas. Since those formulas will reference the cells
containing the parameters/constants of f(x) and g(x), the solutions will
automatically (and conveniently) update when f(x) and g(x) change.
....

If the OP's functions are simple low order polynomials, logarithmic or
exponential functions to begin with, it'd be inefficient for the OP to be
fitting trend lines. And the trend lines aren't necessarily good
approximations for the underlying functions near the point of intersection.
Solver is a manual solution (unless the OP were to use a Calculate event
handler to run Solver whenever the function parameters change upon any
recalc), but it's likely to be more accurate than finding the intersection
point of trend line approximations to the underlying functions.