This is filled with a lot of hand waving bad math, which distracts from some reasonable points.

rule of 70tells us that the time it will take a system or collection to double in size is 70 divided by thepercentage growth rate. The time units depend on how the time over which percentage growthis expressed—like 2%per dayor 2%per year, for instance. The rule works most accurately forsmaller growth rates, under 10%.

Actually showing 1.10^7 = 1.949 vs 1.01^70 = 2.007, so you can approximate by dividing percentage by 70 between 1% and 10% is fine. Stating it as true in the text then adding a note well no not actually latter on is problematic.