\begin{align}
    r_t &= \mathrm{exp}_{r_0} \left(\left(1 - e^{-ct} \right) \mathrm{log}_{r_0}(r_1) \right) \\
    v_r^{(n)} &= c\log_{r_t^{(n)}}\left(\hat{r}_1^{(n)}\right).
    \label{7}
\end{align}
