\begin{axis}[%
  scatter/classes={default={mark=o,draw=black}},
  enlargelimits=true,
  axis x line=center,
  axis y line=center,
  xmin=0,
  ymin=1,
  ]
  \addplot[domain=0:1, blue, samples=100]{.5*exp(x)+.5};
  \addplot[scatter, scatter src=explicit symbolic]
  table {
    x y
      0   1
      0.1 1.05
      0.2 1.1025
      0.3 1.1576
      0.4 1.2155
      0.5 1.2762
      0.6 1.3400
      0.7 1.4071
      0.8 1.4774
      0.9 1.5513
      1   1.6288
  };
\end{axis}
