[laqq3]

Good analysis but small nitpick: the use of "Θ" in Θ(a×exp(R×𝑡)) is slightly inaccurate (or is it the use of "a"?) because the set of functions Θ(a×exp(R×𝑡)) is the same for all positive a.

[s_gourichon]

Well, yes, of course: isn't "a doesn't matter" the core of the point of the parent comment?