Given that adding CO2 increases the growth rates based on the published research between 10 and up to 24X the same growth rate without, what do you think happens to the rate of N uptake for plant growth?
You have 10-24X more growth and usage of C, and plants have about the same C:N ratio.
So it's pretty likely that you also need to scale up the addition of NO3, NH4 is rather toxic and as good inducer of some species of algal spores and NO3 provides a longer easier to dose source of Nitrogen.
Same deal with K+, PO4 etc.
You can add all the CO2 etc in the world, but if you rate limiting step is say, PO4, then you cannot increase growth much by trying to add more CO2.
So, take this same concept and applying it to increases in the world's atmospheric CO2 rise. Do you think that the plants will grow more and suck up the added excess CO2?
Not if they are N, P, K, Fe limited.
So it really depends.
If you are a farmer, and you want to get more out of the added CO2, then adding more Nitrogen fertilizer will be required to maintain the balance between C:N
In our tanks however, adding NO3, K, etc is easy and cheap.
So we casn easily and cheaply maintain a nice buffer range of nutrient levels so that they never run out.
That way we get the most of the nutrients, and the CO2.
More importantly, now we also get the maxmum growth rates out of the least amount of light.
Less light = less cost, less nutrient demand, less work, less initial cost, less heat, more stable over the long term.
Thus "a light limited tank" is a good way to think of the system.
We have N limited, P limited, trace limited, CO2 limited methods to modulate growth rates, but light is where it all starts and is the main driver of all photosynthetic growth.