Final answer:
Mutating a gene's promoter can either increase or decrease transcription by affecting how transcription factors and RNA polymerase bind to the promoter, influencing the gene expression regulation.
Step-by-step explanation:
The question involves the concept of regulating gene expression by altering the properties of a gene's promoter. Mutated promoters can increase or decrease the rate of transcription by changing how transcription factors and RNA polymerase bind to the DNA. A stronger promoter would lead to increased transcription because RNA polymerase would have a higher affinity for binding. Conversely, a weaker promoter could reduce transcription rates. In the specific context of E. coli, the sigma (σ) factor associated with RNA polymerase is crucial for recognizing promoters and initiating specific gene transcription.