The text describes the increasing order of function growth rates: log n, n, n log n, n², n<sup>k</sup>, 2<sup>n</sup>. For small n, the order may not hold, but for large n, 2<sup>n</sup> grows fastest, exceeding all others. The ordering is crucial for algorithm analysis. This segment clarifies a crucial point about the relative growth of functions like n<sup>100</sup> and 2<sup>n</sup>. The speaker emphasizes that while for small values of 'n', n<sup>100</sup> might appear larger, as 'n' increases significantly, 2<sup>n</sup> eventually surpasses n<sup>100</sup> and continues to grow at a much faster rate. This highlights the importance of considering the behavior of functions for large input sizes in algorithm analysis, where efficiency is paramount.