Why is it beneficial for e. coli to have the ability to regulate the expression of the lac genes, rather than just express them all the time?

Because it prevents bacteria from wasting energy and allows bacteria to use lactose as a carbon source.

Explanation:

Escherichia coli can use lactose as a carbon source through the lac operon. This way the necessary enzymes are only synthesized when lactose is present, saving bacteria from wasting energy unnecessarily.

In the absence of lactose, the lac operon may turn on a repressor, lac repressor, which prevents transcription, avoiding energy expenditure. The lac repressor is encoded by the lacI regulatory gene. When lactose is added to the cells, the lac repressor changes its conformation, reducing its affinity for the lac operator. Thus, RNA polymerase initiates the transcription of lacZYA genes. These genes are expressed for the expression of enzymes responsible for the capture and metabolism of lactose by the bacterial cell.

"d.) carbon dioxide and hydrogen sulfide"

i think its y= -4x-14