For a polymer solution, the dependence of viscosity $(\eta)$ on shear rate $(\dot{\gamma})$ is described by the three-parameter Carreau model given by
\[
\eta=\eta_{0}\left[1+(\lambda \dot{\gamma})^{2}\right]^{(n-1) / 2}
\]
where, $\eta_{0}, \lambda$, and $n$ are the three parameters of the model. Here, all three parameters are positive quantities. As the shear rate increases from $1 \mathrm{~s}^{-1}$ to $100 \mathrm{~s}^{-1}$, the viscosity of the polymer solution decreases by a factor of $10$. For a polymer solution with $n=0.4$ and $\eta_{0}=15 \mathrm{~Pa} \mathrm{~s}$, the value of the parameter $\lambda$ is __________ s $\text{(rounded off to two decimal places)}$.
