Solve for parameters of an Exponential Function from 3 points

Questions
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1

Hi
I am rather new to mathematica.
I want to find a numerical solution for the parameters a, b and c in the exponential function of type

y=a*exp(-b * x)+c

when three points are given: (x1,y1); (x2,y2); (x3,y3);

I tried several functions, such as:

SolveAlways[{y1 == a*Exp[-b * x1] +c , y2 == a*Exp[-b * x2]+c , y3 == a*Exp[-b *x3]+ c },{a,b,c}]

which was not successful, however.

Is there a way to solve this using Mathematica?

Thanks in advance,
Michael

2

Define

y[x_] := a E^(- b x) + c

then enter 6 numerical values for x and y and do

NSolve[{y[x1] == y1, y[x2] == y2, y[x3] == y3}, {a, b, c}]