Pokemon-go – What trainer level do you have to be to max “power up” a pokemon

My data isn't complete as I haven't been actively keeping track, but here is what Iv'e found. Once you reach max CP for any Pokemon at your level, every subsequent level allows you to power up said Pokemon twice. Each power up grants 20-60(level 4-16) CP based off of the Pokemon's initial power and player level. My Lapras maxed out at 971 at level 11, 1056 at level 12, ~1140 (forgot screenshot) at level 13 and 1267 at level 14. +85, +~90, +~120. I have since run out of Lapras candies so i can't pursue this information further until i obtain more. I'll attempt to gather more data using a more common Pokemon later (Eevee evolution probably) and edit when i can, but the stardust needed is hard to maintain.

How this relates to the question:

The encounter CP is a random number between lowest possible (10 in 1st evolution) and maximum possible. From the data we can see that the max CP does increase incrementally so as a result encounter CP will increase at the same rate.

In conclusion, while it is more effective to power up and evolve Pokemon later, the max CP increase seems to be mild enough that from level to level the difference isn't insurmountable.

As you level up your trainer level by catching pokemon, hatching eggs, stopping at pokestops, etc. You will find out that this will also increase your max CP for your pokemon. For example I was level 12 and my max CP for my pidgeot was 744, now I am level 13 I can boost him to the next MAX CP that I have obtained.

TIP: However this can be bad because you will use more resources than needed (seeing as the more you power up the more it costs every boost). You might want to evolve the pokemon with the highest CP and just keep replacing the pokemon until a respectable MAX CP can be obtained and you have higher CP pokemon to catch(so you boost while the cost is low on a higher level CP).