[maxerickson]

My question is about how much r matters.

For influenza, each infected cell apparently infects ~22 other cells:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1563736/

So in 2 generations you have 500x the virus.

If it were 'less' exponential, and each cell only infected, say, 5 others, then you get to 500x late in the 4th generation.

In a cartoon example where a low exposure leads to 1 infected cell and a high exposure leads to 500 infected cells, the low exposure matters more if the reproductive factor is lower.