Question

Y(x) = A exp(-Cx) + B

The Vernier Labquest returns the Natural Exponent curve fit using A, B, and C variables. What information is found in the numerical values of the fitting parameters ie, what do A, B, and C mean?

Answer 1

Answer:)

The various parameters used in the fitting of the natural exponent curve all have different impacts on the graph, and the behavior, of Y(x):

1. A : the parameter A (along with B) controls the point where the function intersects the Y axis. This can also be interpreted as the output in the case of zero input. This can be seen as follows :-
   
2. B : the parameter B controls the value that the function Y(x) settles to as x tends to very large values. One may think of B as the offset from the x-axis.
3. C : this parameter controls how fast Y(x) decays (or increases, if C < 0) to the value at large x (dictated by B). We may see this from :
   
   Thus, at any given point, the derivative is dependent on the value of C, and this says that the decrease or increase of the function is dictated by C (and to a small extent, by A).