We study the emergence of power-law behavior in populations whose top 
performances grow exponentially in time. Motivated by a detailed analysis 
of the entry, upgrade, and exit pattern of nodes on the TOP500 
super-computer lists over the last 16 years, we propose a dynamical model 
for the population in which performances of existing nodes are copied or 
improved upon following a probabilistic rule. We show that the model can 
be mapped exactly to the randomly branching tree problem in statistical 
physics and affords a traveling wave solution, in agreement with the 
observed behavior. A number of interesting properties emerge from the 
analytic solution. In particular, the top performers may still improve 
exponentially even when the population as a whole is on a declining path. 
Dynamic correlations in the performance-rank list over the years 
are also discussed through exact calculations of suitable two-point
distribution functions. Our study offers a quantitative framework to 
relate the individual-level performance pacing to the population-level 
rank distribution which could be of interest in a broad range of ecological, 
social and economic contexts.