A microbial culture, with a specific growth rate of $\mu_{1}$ (per hour), is being grown in a continuous reactor at steady state with hydraulic retention time (HRT) of $24$ hours. This reactor is subjected to a perturbation by reducing the HRT to $12$ hours. The reactor recovers from the perturbation and comes to a new steady state with a new specific growth rate of $\mu_{2}$ (per hour). Which one of the following statements is correct?
- $\quad \mu_{1}=\mu_{2}$
- $\quad \mu_{1}=0.5 \mu_{2}$
- $\mu_{2}=0.5 \mu_{1}$
- $\quad \mu_{2}=e^{0.5} \mu_{1}$
