There is also the relative speed at which clones are produced vice droids: Confederate growth curves are for droids, where as the curves for the Grand Army of the Republic are for the number of cloning tanks. The increase in size of the Confederate Droid Army is immediate, while the expansion of the Grand Army of the Republic must also add on thetime to raise the clones. Logically there is also an additional step in the growth process for the Grand Army. While clones produced from a hatchery can theoretically be used to construct more factories to achieve exponential growth, the cost, speed and efficiency compared to droid labor make this a poor choice. The only way for them to achieve exponential growth is to have a factory produce droids that go one to both build hatcheries and more factories. This formula would follow
dt = {0.693*sqrt[Tl*Tf*Wf /(1-Ft)]}+Tc
where dt is doubling time, Tl is the time to build a labor droid, Tf the time to build a droid factory, Wf the workforce to build a factory, Ft the fraction of droids building cloning tanks, and Tc the time to grow and train a clone.
As the Kaminoans knew that this army was for the Republic (Attack of the Clones) they would be aware of the scope of the conflict. And as they have made other clone armies (Lama Su noting this was one of their finest in Attack of the Clones) they would be aware of the number required to realistically fight. Thus even if their initial production capabilities were not able to match the requirements of a galaxy spanning war, they would almost certainly follow the above model so that their ability to produce would increase exponentially, and then when the clones were fully grown the size of the army would increase as well. By following this philosophy, even if the initial total strenght of the army was 200,000 clones the final strength could easily exceed several quadrillion. This appears to be the case as Kamino is described as having cloning centers in cities spread across the world (Star Wars: Complete Locations) and we know that as the war progressed they continued to increase the number of hatcheries, including building secret hatcheries on Coruscant. (Odds) We further know that the Republic continually received deliveries of clone troopers – Jedi Trial speaks of reinforcements soon to be delivered from Kamino. And while the Republic was stretched thin in Labyrinth of Evil, months later it had billions of clones to spare for the Systems Governance Decree in Revenge of the Sith.
However, this raises issues with the carrying capacity of Kamino – if it takes a decade to grow and train clones, how does the biosphere of a single planet support them? Kamino has a long history of importing food and supplies, but the increase in the volume required would attract attention and the army is intended to be a secret. A sharp incline in the number of shipping contracts and the price of commodities relevent to sustaining a megaopolis scale planet would certainly be noted by someone, even if it were just a common stock broker. Thus they would be limited to what the Kamino system can provide itself.
But this is not necessarily a population limit if the clones are not constantly consuming resources. Clones can be placed in suspended animation (Clone Wars: The Defense of Kamino; Republic Commando: Hard Contact) when not needed. While it may be possible for them to still receive “flash training” from the “neural pumps” (Republic Holonet News 15:2:22, “Clone Commander Graduates Ready for Action” SW Insider 74, page 66; Republic Commando: Triple Zero; Dark Force Rising) used for their education in this state, a greater possibility is that clones are grown and trained very quickly, and then are placed in hibernation until needed.
This would fit with what was established by canon. While many sources attribute the growth period to being approximately a decade (Republic Commando: Hard Contact; The Cestus Deception), these sources are almost uniformly speaking of ARC troopers and Clone Commandos, who experienced in depth training with drill sergeants (Republic Commando: Hard Contact; The Cestus Deception; Republic Command: Triple Zero) for many years. That Lama Su states all clones take this long in Attack of the Clones is unsurprising, the Kaminoans are businessmen and are known to try and pass off their advanced model clones as the stock unit to encourage more sales (The Pengalan Tradeoff). We know clones can be “produced in a few weeks” per The Dark Empire Sourcebook, so the limit is not the technology, but rather their training. Regular clone troopers are only mentioned to being subjected to “neural pumps” (Republic Holonet News 15:2:22, “Clone Commander Graduates Ready for Action” SW Insider 74, page 66) and “flash-training” (Republic Commando: Triple Zero) to provide all their basic training. Further, we observe that clone troopers are grown in far less time - Labyrinth of Evil mentions that clones seen freshly started two months into the war had been received. The growth time for a clone can be estimated from that of Commander Bly; the NCO Alpha-17 trained him before Bly was assigned to General Secura. Alpha-17 departed for Kamino in month 15 of the war (Clone Wars: The Best Blades), and Bly participated in the mission to Honoghr in month 16. (Clone Wars: On the Field of Battle) This gives his growth and training a time of 1 month, which matches the statement in The Dark Empire Sourcebook. This number is supported in Republic Commando: Triple Zero where they expect to have clones to train in a month when Jango returns to Kamino. While this time is at odds with what Talon Karrde’s information suggests (The Last Command), one must remember that the Kaminoans were highly secrative. That clones can be grown so rapidly is unsuprising both scientifically and in the Star Wars universe; Kal Skirata expected that the young Null series clones he took as his wards had spent an exceptionally long time in cloning tanks to achieve their apparent age, he was only shocked when he learned the aging process was not restored to normal once they were outside the tanks (Republic Commando: Triple Zero). It is interesting that the clones grew almost ten times faster then normal humans while in the the hatcheries, but ages only twice as fast once decanted (Attack of the Clones Visual Dictionary). Thus it appears that clones can be grown rapidly in tubes but it is their training that takes years.
Even if it is a matter of weeks instead of years, the additional time required to produce clones instead of directly producing droids was clearly a concern. This raises an interesting point – to prevent the Republic from being rapidly overwhelmed by faster produced droids, one would surmise that the initial strength of the Grand Army of the Republic must be far greater then that of the Confederacy. This is a fact confirmed by Lord Tyrannus in a public address when he states, “The forces on our borders and outlying colonial assets are admittedly facing greater numbers" (CIS Shadowfeed 14:2:14, article "Dooku Addresses 'Spurious' Republic Reports" SW Insider 65, page 75). However continual casualties would remove that advantage and inspire them to reduce this handicap as much as possible, which is what they did. Sixteen months into the war the Republic prototyped a new kind of clone vat commonly known as the Spaarti cylinder. These new hatcheries cut the growth time down to one tenth the time required by the original method (The New Essential Chronology). This throws off the above formula so it would have to be recalculated to function beyond this point.