Cellular adaptability to environmental changes depends on the collective actions of genes, mRNA, proteins and ligands, all of which are components of a ''genetic network''. To understand the dynamics of a gene network in response to temporally and spatially environmental changes, we focus on the galactose utilization network in the yeast Saccharomyces cerevisiae. This network allows yeast cells to metabolize galactose in the absence of glucose and is tightly repressed when glucose is available in the environment. The main question is how the Gal network is activated when glucose is depleted since both sugars cannot be metabolized simultaneously. Using a microfluidic device, we supplied yeast cells with both glucose and galactose before linearly depleting glucose at different rates. We tracked the onset and accumulation of a yellow fluorescent reporter-tagged Gal1p, the first enzyme of the Gal network. Our data shows that the glucose-depletion rate plays an important role in the activation of the Gal network. The onset of the network's activation depends on the time it takes to pass a specific threshold of the glucose concentration. On the other hand, the full induction of the Gal network, represented by the Gal1-accumulation time, is strongly influenced by the depletion rates. In particular, the mean of the Gal1-accumulation time increases significantly when glucose is depleted instantaneously. Furthermore, the variability of the Gal1-accumulation time also increases in short depletion rates and achieves a minimum at intermediate depletion rates. Using a mathematical simulation, we demonstrate that the increase in the accumulation time is due to the loss of energy when glucose is instantaneously depleted. This loss of energy also correlates with the length of diauxie, a period of catabolic transition from glucose to a secondary carbon source. Thus, changes in the glucose-depletion rate not only affect the dynamics of the Gal network's activation, but can also affect the phenotypic outcomes of the single cells within the population. Our results contribute to growing sets of evidence that a gene network can exhibit complex, dynamic behaviors under environmental changes to shape the fitness and survival of individual and collective members of a microbial population.