[rocqua]

You might want an upper limit, so either logistic growth [1] or something like 1 - exp(-(T + T_0)) feels like it makes more sense.

I especially like logistic growth for having slow growth at the start and end, only growing quickly in the middle.

[1] https://www.khanacademy.org/science/biology/ecology/populati...

[SomeStupidPoint]

You don't need an upperbound as long as your function is sufficiently slow growing.

Example:

Log(years) doesn't have a bound, but is unlikely to cause problems over any reasonable time scale.