Explain how this enables the bacterium to detect the population density

"When autoinducers produced by one bacterium cross the membrane of another, they bind to receptors in the cytoplasm. This autoinducer/receptor complex is then able to bind to DNA promoters and activate the transcription of quorum sensing-controlled genes. In this way, individual bacteria within a group are able to benefit from the activity of the entire group."

The concentration of chemical auto inducers increases with increase in population density

Explanation:

There is something known as Quorum sensing which is a sort of cellular communication in bacteria established through chemical signals. A bacterium is enabled to observe/monitor the environment and thus produce a widespread change in the species with in a community. These sensing processes are effective only when large numbers of cells are doing sensing controlled process together. A bacteria releases auto-inducers whose concentration increases when the population density of cells increase.