If you mean with respect to time, wrong. The denonimator in adoption rate that makes it a “rate” is the number of existing businesses, not time. It is adoption scaled to the universe of businesses, not the rate of change of adoption over time.
One could try to make an argument that "adoption rate" should mean change in adoption over time, but the meaning as used in this article is unambiguously not that. It's just percentages, not time derivatives, as clearly shown by the vertical axis labels.
Yes, it charts the adoption rate (adopting firms/firms) against time. But it doesn't use the term "adoption rate" to mean the first derivative of "adoption" with respect to time.
When it talks about the adoption rate flattening it is talking about the first derivative of the adoption rate (as defined in the previous paragraph, not as you wish it was defined) with respect to time tending toward 0 (and, consequently, the second derivative being negative.) Not the third derivative with respect to time being negative.
I assure you I don't have any wishes one way or another.
What tickled me into making the comment above had nothing to do with whether adoption rate was used by the author (or is used generally) to mean market penetration or the rate of adoption. It was because a visual aid that is labeled ambiguously enough to support the exact opposite perspective was used as a basis for clearing up any ambiguity.
The purpose of a time series chart is necessarily time-derivative, as the slope or shape of the line is generally the focus (is a value trending upward, downward, varying seasonally, etc). It's fair to include or omit a label on the dependent axis. If omitted, it's also fair to label the chart as the dependent variable and also to let the "... over time" be implicit.
However, when the dependent axis is not explicitly labeled and "over time" is left implicit, it's absolutely hilarious to me to point to it and say it clearly shows that the chart's title is or is not time-derivative.
I know comment sections are generally for heated debates trying to prove right and wrong, but sometimes it's nice to be able to muse for a moment on funny things like this.
> Adoption rate = first derivative
If you mean with respect to time, wrong. The denonimator in adoption rate that makes it a “rate” is the number of existing businesses, not time. It is adoption scaled to the universe of businesses, not the rate of change of adoption over time.