'grow faster' is a bit of a vague statement. What we should be talking about is biomass added, which is what sequesters carbon. Older trees unequivocally add mass at a faster rate, which is geometrically obvious when you consider that old growth tree rings add about the same radius each yeah that young growth trees do, and then consider that area of a circle grows with the square of radius.

see:

https://news.unl.edu/newsrooms/today/article/study-finds-lar....