Final answer:
A mutation in one of the BRCA1 genes that inactivates the gene is likely to increase the rate of cell division due to the failure of the tumor suppressor function, leading to uncontrolled cell division, a common feature of cancer cells.
Step-by-step explanation:
If a cell has a mutation in one of its BRCA1 genes that inactivates the gene, this would likely lead to an increase in the rate of cell division. BRCA1 is a tumor suppressor gene, which means it plays a role in DNA repair and helps to maintain the stability of a cell's genetic information. When such a gene is not functional, DNA damage may not be properly repaired. This can contribute to the accumulation of mutations which can lead to cancer. In essence, when the BRCA1 gene is inactivated, cell-cycle control mechanisms are compromised, and this can result in uncontrolled cell division — a hallmark of cancer.
A mutation in genes like BRCA1 does not guarantee that cancer will develop, as other genetic factors and environmental influences also play a role. However, it does increase the risk, and a non-functional BRCA1 contributes to a cell's journey towards malignancy. The BRCA1 mutation itself can contribute to cancer development by allowing DNA damage to accumulate. Thus, while the immediate impact on cell division rate may vary and depend on other factors, the overall tendency is for an increase, as the regulatory mechanisms for cell division are disrupted.