According to the latest update from Apple on iOS 9 install numbers, the rate of adoption is steadily and quickly increasing. The latest numbers show that the latest iteration of iOS is now installed on 61% of devices. This comes just 5 weeks after iOS 9's initial release on September 16.
For comparison, iOS 8 held an install base of 52% right around this same time last year. Currently, iOS 8 stands at 30%, while older versions, from iOS 7 and earlier, are holding onto a 9% share.
It's perhaps not much of a surprise that iOS 9 has enjoyed rapid adoption, as its smaller update size helps to alleviate many of the issues that users of smaller-capacity iPhones faced with the large update to iOS 8 last year. Throw in a pair of new iPhones with the iPhone 6s and iPhone 6s Plus, along with availability to a large range of earlier iPhones, and you have a recipe for quick adoption.