Consider a reaction that is first order in both directions

$\mathrm{A}\underset{{\mathrm{k}}_{\mathrm{b}}}{\overset{{\mathrm{k}}_{\mathrm{f}}}{\rightleftharpoons }}\mathrm{B}$

Initially only $\mathrm{A}$ is present, and its concentration is ${\mathrm{A}}_0.$ Assume ${\mathrm{A}}_{\mathrm{t}}$ and ${\mathrm{A}}_{\mathrm{eq}}$ are the concentrations of $\mathrm{A}$ at time $"\mathrm{t}"$ and at equilibrium, respectively. The time $"\mathrm{t}"$ at which ${\mathrm{A}}_{\mathrm{t}}=\left({\mathrm{A}}_0+{\mathrm{A}}_{\mathrm{eq}}\right)/2$ is: