The objective of this work is to infer the biomass and product concentrations in a class of bioreactor, under the assumption of substrate measurements. This is done by employing a mathematical model of a continuous stirred bioreactor where the corresponding kinetic term is experimentally corroborated. The observer's structure contains, as usual, a predictive term given for nominal model plus a corrective term, which is proposed as adaptive one, where the corresponding observer's gain obey a specific dynamic equation, which provides an exponential convergence characteristic, under the Lipschitz assumption of the system. Numerical simulations show an adequate performance of the proposed observer and a comparison with a finite-time observer is done.