A continuous, stirred tank reactor is initially filled with solvent. At \(t=0\), reactant, A, is fed into the tank at a rate of \(\dot{v}_{a o}\left(\mathrm{~m}^{3} / \mathrm{min}\right)\). The concentration of \(\mathrm{A}\) in the feed is \(c_{a o}\left(\mathrm{~mol} / \mathrm{m}^{3}\right)\). Compound \(\mathrm{A}\) undergoes a first-order decomposition reaction with a characteristic rate constant of \(k^{\prime \prime}\left(\mathrm{min}^{-1}\right)\). For a tank of overall volume, \(V_{o}\), what is the concentration of \(\mathrm{A}\) in the tank as a function of time?