Food is the only limiting factor that keeps populations from growing too large

No, I don't think this is true,

Some other factor for example is female empowerment: more and more women choose not to have children or to have fewer children.

Also, housing could also be a factor: many families could decide against new children even if they can feed them, if their house is too small (think 40 Square meters and they already have 2 childen).

productive most commonly means: achieving or producing a significant amount or result.

explanation:

productive can also mean:

producing or giving rise torelating to or engaged in the production of goods, crops, or other commodities.

these depend on how the word productive is used. most likely productive will mean   achieving or producing a significant amount or result.