It is easiest to do this by starting with the symbolic toolbox.
C = sym('C', [1 2]);
Then
residue = sum( (C(1)*exp(C(2)*x) - y).^2 );
fun = matlabFunction(residue, 'vars', {C});
Now you can fminsearch using fun as the objective function.
The more direct method without searching is
temp = [ones(length(x),1), x.'] \ log(y.');
C1 = exp(temp(1));
C2 = temp(2);
