Step 1: Carothers Equation.
The Carothers equation establishes a relationship between the average degree of polymerization and the extent of reaction in step-growth (condensation) polymerization. It is also instrumental in predicting gel formation during the polymerization process.
Step 2: Option Analysis.
- (A) Accurate: The Carothers equation is applicable to condensation (step-growth) polymerization. - (B), (C), (D): These mechanisms (chain growth) are not directly addressed by the Carothers equation.
Conclusion: \[\boxed{\text{A) condensation polymerization}}\]