The primary function of adaptation is to deal with systems with uncertain and time-varying dynamics. However, a natural question is: how fast must the rate of change of the uncertain dynamics be, before it can no longer be captured by adaptation? In order to initiate an understanding of this problem, we consider in this paper a first-order linear system with time-varying unknown parameters modeled as a finite state hidden Markov chain, It is shown that the key factor inherent in characterizing the capability of adaptation is the information uncertainty coupled with the structural complexity of the systems under control, rather than the existence of a certain critical rate of parameter changes that has been conjectured by many in the area.