% Thanks to Jake: http://tex.stackexchange.com/a/142815/5645
\begin{tikzpicture}
    \draw (0,0) circle [radius=1];
    \draw [domain=1:18.8,variable=\t,smooth,samples=200,->,>=stealth']
        plot ({\t r}: {1+2*exp(-0.1*\t)});
\end{tikzpicture}