Question

curve fitting of y=ab^x​

Answer 1

home Exponential Curve Fitting contact

Introduction

This article describes the exponential curve fitting method implemented in Graphics-Explorer.

Graphics-Explorer is a function- and equation grapher program, that allows for experimenting

with functions and equations.

By simple mouseclicks points may be added to the screen.

Then the the best fitting poynomial- or exponential function may be calculated.

Calculation of the several type of exponential functions takes place in unit "expfuncUnit".

However, some other units are used, such as the

- scaleUnit: supplies scaledY, the distance between two vertically adjacent pixels in the coordinate system.

- least-square unit, which holds procedures

- BuildExp12(var PP : puntarray)

- BuildExp3(var PP : puntarray)

- puntenUnit, which holds an array punten with all (x,y) pairs. Maxpunt holds the number of entries in punten[ ].

Note: punt is Dutch for point. Punten is Dutch for points.

type TPunt = record

x : double;

y : double;

end;

var punten : array[1..40] of TPunt;

The complete source code of the ExpFuncUnit you can find [ here ].

The following types of exponential functions are supported:

1... y = abx + c

2... y = aebx + c

3... y = eax2+bx+c

4... y = abx

5... y = aebx

Note: e is the base of the natural logarithm, e = 2.718.......

A simple general form of an exponential function is..........y = a.gx

For x = 0, y = a, the "start" value.

g is called the growth factor.

Exponential functions are the result of constant relative growth.

Each time x increases by 1, y is multiplied by g.

Note: absolute growth is the result of addition, relative growth is the result of multiplication