NO serial number tag? look for last digit of serial, if you can't find a specific mention of "Type" on the tag , looks like they are types 1 through 7 and you can maybe trim the list down if you have some good idea of how old it is , you can go through the list of parts catalogs
https://www.ereplacementparts.com/searc ... rer=Poulan and see if anything "stands out" as being unique to a newer or older type (generally older type may have no chain brake, but instead just a hand guard, newer types may have increasingly complex anti-tamper screws, carburetor model and brand if original carb, can sometimes give a clue if you can figure what year they first used that carburetor model, etc. However, most fuel system parts (pre-2012) will generally be all the same.. most type variations came up when they had to alter emissions parts, ignitions, safety designs, etc.
How poor are they who have not patience. What wound did ever heal, but by degrees? - Iago (Othello Act II, Scene 3)