In a process called quorum sensing, bacteria monitor their population density via extracellular signaling molecules and modulate gene expression accordingly. This paper describes a one-dimensional model of a growing Pseudomonas aeruginosa biofilm. Quorum sensing has been included in the model by the addition of equations describing the production, degradation, and diffusion of acyl-homoserine lactones in the biofilm. In order for quorum sensing to initiate near the substratum, in accordance with experimental observations, model results suggest that cells in oxygen-deficient regions of the biofilm must still be synthesizing the signal compound. This result highlights the importance of careful study of the relationship between metabolic activity of the bacterium and signal synthesis.