It has been an ongoing scientific debate whether biological parameters are conserved across experimental setups with different media, pH values, and other experimental conditions. Our work explores this question using Bayesian probability as a rigorous framework to assess the biological context of parameters in a model of the cell growth controller in You et al. When this growth controller is uninduced, the E. coli cell population grows to carrying capacity; however, when the circuit is induced, the cell population growth is regulated to remain well below carrying capacity. This growth control controller regulates the E. coli cell population by cell to cell communication using the signaling molecule AHL and by cell death using the bacterial toxin CcdB. To evaluate the context dependence of parameters such as the cell growth rate, the carrying capacity, the AHL degradation rate, the leakiness of AHL, the leakiness of toxin CcdB, and the IPTG induction factor, we collect experimental data from the growth control circuit in two different media, at two different pH values, and with several induction levels. We define a set of possible context dependencies that describe how these parameters may differ with the experimental conditions and we develop mathematical models of the growth controller across the different experimental contexts. We then determine whether these parameters are shared across experimental contexts or whether they are context dependent. For each of these possible context dependencies, we use Bayesian inference to assess its plausibility and to estimate the parameters of the growth controller. Ultimately, we find that there is significant experimental context dependence in this circuit. Furthermore, we also find that the estimated parameter values are sensitive to our assumption of a context relationship.