I've constructed a growth scenario for an energy model and rather than use linear or exponential growth, I'm applying a linear increase rate to the increment amount, not to the base amount.
It's a best fit approach to what I'm looking to achieve with the model, hitting a target capacity in 2030 but starting out with a similar install rate as exists at present.
It's certainly non-linear growth, but it's not strictly exponential growth either (since it's not of the $\boldsymbol{x^n}$ type of geometric equation). Arithmetic growth seems to be defined as linear growth, so that's not arithmetic or geometric I figure.
It's a bit hard to talk about not knowing the correct maths expressions to use so I want to define terms using an example.
I'm asserting that installed Rooftop PV in my state will increases at the rate defined as capacity added in year Y as:
$$Y_n = 257 + 12\times \boldsymbol{n}, \;$$ $\qquad$where $\boldsymbol{n}$ is the number of years after 2019.
if $C_\boldsymbol{n}$ is the cumulative total at year $\boldsymbol{n}$,
$$ C_\boldsymbol{n} = 1387 + \boldsymbol{n}(257 + 12\times \boldsymbol{n})$$ $$\Leftrightarrow C_\boldsymbol{n}=12 \boldsymbol{n^²} + 257\boldsymbol{n} +1387$$
$$\Rightarrow C_\boldsymbol{n} \approx \frac{\boldsymbol{n}^2 + 21\boldsymbol{n} +116}{12}$$
So can I call it quadratic growth? Does that have common usage enough to be understood in scientific literature around renewable energy?
Here's what it looks like in a table applied year on year for a decade:
Looking at the last 5 years there's an average (exponential) growth rate of 24.5%. I've plotted both the annual additional installs and the annual cumulative installed capacity and the 24.5% fits reasonably for both of them the the historical numbers for 2015-19.
If I project that out as exponential growth it quickly gets to improbably (impossible) amounts in a decade, so exponential growth is not a growth construct I want to use, even using a low rate because the curve is problematic from several practical perspectives.
The graph below plots various rates of change for the additional capacity p.a.
The graph below plots those same rates of change but showing the cumulative installed capacity.
Since you have already shown that the quantity can be described by a quadratic equation, yes, it is quadratic growth.