fitnlm giving Inf or NaN values

I am trying to use fitnlm to fit a range of equations to data. It works fine for a power relationship, e.g.

modelfun = @(b,x) b(1)*x.^b(2);
beta0 = [1 1];
X=[1694 3000 3464];
Y=[0.556167635253459 1 1.13624749173126];
mdl = fitnlm(X,Y,modelfun,beta0);

But I am getting errors for an exponential:

modelfun = @(b,x) b(1)*exp(b(2)*x);
beta0 = [1 1];
X=[1694 3000 3464];
Y=[0.556167635253459 1 1.13624749173126];
mdl = fitnlm(X,Y,modelfun,beta0);
%But I get this error
% Error using nlinfit>checkFunVals (line 649)
% The function you provided as the MODELFUN input has returned Inf or NaN values.
% 
% Error in nlinfit (line 251)
% if funValCheck && ~isfinite(sse), checkFunVals(r); end
% 
% Error in NonLinearModel/fitter (line 1127)
%                     nlinfit(X,y,F,b0,opts,wtargs{:},errormodelargs{:});
% 
% Error in classreg.regr.FitObject/doFit (line 94)
%             model = fitter(model);
% 
% Error in NonLinearModel.fit (line 1446)
%             model = doFit(model);
% 
% Error in fitnlm (line 99)
% model = NonLinearModel.fit(X,varargin{:});

I chucked the same values in Excel and it can create an exponential relationship no problem, but I have 336 relationships to derive so I'd rather do it in Matlab! :) I would also like to try this equation, which runs through with these values with a warning the model is overparameterised, but on one of the full sets (not given here for space) I get the same error as above.

%y=a((x+c)^b)
modelfun = @(b,x)b(1)*((x + b(2)).^b(3));
beta0 = [1 1 1];
X=[1694 3000 3464];
Y=[0.556167635253459 1 1.13624749173126];
mdl = fitnlm(X,Y,modelfun,beta0);

Any idea where I am going wrong?

Thanks for your help!

[Torsten]

Do you know how big exp(1694), exp(3000) and exp(3464) are ?

If yes, then why do you start with beta0(2) = 1 ???

[Catriona Fyffe]

Fair point, hadn't thought of that!

[Catriona Fyffe]

Great, so if I do this, it works! Hahaha, thanks!

modelfun = @(b,x) b(1)*exp(b(2)*x);
beta0 = [1 0.00001];
X=[1694 3000 3464];
Y=[0.556167635253459 1 1.13624749173126];
mdl = fitnlm(X,Y,modelfun,beta0);

[Torsten]

For the third model equation, you have 3 data points to determine 3 parameters.

Usually, you should get parameters that reproduce the data exactly. But this is not fitting, but interpolating. The parameters have no physical significance.

Why for the third model function you get the same error as above for a larger dataset, I can't tell. Maybe because x+b(2) becomes negative. Then (x+b(2)).^b(3) becomes complex-valued.