It has been years since I have taken any math, but I have come across a problem in my job where I need to chart a line that (as currently plotted) is asymptotic to the X-axis and arcs up.
How do I derive an equation for this line? The data points fall in a fairly good pattern but don’t line up exactly. If I was plotting a straight line, I know how I’d do it, but I don’t remember how to with a curve.
Any help would be appreciated (and if I’ve left something critical out, let me know). Thanks!
You mean it’s asymptotic with the x-axis to the left, but as it goes right (positive), it arcs up? This would be the exponential function, y=ke^(ax). If you take the logarithm of the y-values before you plot it, you can then fit a straight line through it.
If the curve you’re talking about is asymptotic to the right, and goes up as it approaches zero (IOW, also asymptotic to the y-axis), that is the y=1/x curve, you can fit a straight line by taking one over the y-values first.
Okay, first try plotting ln(y) vs x; if y = exp(Ax+B), then ln(y) vs x will give you a straight line (ln(y) = AX+B).
Also try plotting ln(y) vs ln(x), if y = Ax[sup]n[/sup] then ln(y) vs ln(x) will give you a straight line instead (ln(y) = ln(A) + nln(x)).
If it’s diverging near the x axis, the latter is probably the one you want. It is, of course, entirely possible that it’s neither a simple exponential nor a simple power, in which case things just got a whole lot harder.
Alternatively you can use the negative arctangent function shifted up by pi/2.
You could try using the Least Squares Method.
There are an infinite number of curve equations so there is no one simple answer. If the curve follows some law then you might find a specific function (exponential, log, whatever) which represents the curve but as a general rule for finding a function you would be looking for polinomials and even then there are many ways of going about it. Personally I have used Chebyshev’s polinomials in the past but there are many others you can use.