I want to create an e-function. For that I created a basic framework for my formular. It looks like this: $$f(x)=ae^{bx}+c$$
After that I determined 3 fix points, which should sit on the function:
$K=(3500,1)$, $L=(500,-1)$ and $M=(2000,0.4)$
Then I inserted the x and y values into the basic function and got these functions:
$(I)\qquad 1=ae^{3500b}+c$
$(II)\quad\enspace -1=ae^{500b}+c$
$(III)\quad 0.4=ae^{2000b}+c$
I did eliminate the 'c part', but then I don't know how to continue:
$(IV)=(I)-(II)\qquad 2=ae^{3500b}-ae^{500b}$
$(V)=(II)-(III)\quad -1.4=ae^{500b}-ae^{2000b}$
I created the function in GeoGebra Classic and the approximate values are:
$a=-3.3$
$b=-0.0004$
$c=1.8$
But how can I get the exact values
(GeoGebra Classic for iPad)
