steep decay curve fitting

hi All,

I have a set of data would like to fit with some simple functions. Can someone please help?

Thanks, Allan

X 100 213 453 969 2070 3133 4741 7175 10859 16436 24877 37652 56989 80499 100000

Y 4711 1872 891 496 315 262 227 205 191 182 176 171 166 164 162

Answer 1

[Star Strider]

One possibility (of an infinite number of possible models):

X =  [100 213 453 969 2070 3133 4741 7175 10859 16436 24877 37652 56989 80499 100000];
Y =  [4711 1872 891 496 315 262 227 205 191 182 176 171 166 164 162];

f = @(b,x) b(1).*exp(b(2).*x) + b(3);
SSECF = @(b) sum((Y - f(b,X)).^2);
[B,SSE] = fminsearch(SSECF, [5000; -1; 1]);

xv = linspace(min(X), max(X));

figure(1)
plot(X, Y, 'bp', xv, f(B,xv), '-r')
grid

The best model is one that accurately describes the process that produced your data. Only you know what that process is.