positive pregnancy tests post medical abortion

hi :) i had a medical abortion exactly a month ago, and at two weeks and three weeks post i got positive tests. not super dark or anything but for sure positive. i know that the hormones do stay in your body for a while, so the two week positive didn't concern me but the three week one kinda did. i have my follow up soon and i'm going to take another test out of curiosity but for anyone who's been testing post abortion did the hormones stay in your body for a while as well? all my pregnancy symptoms went away immediately and i have had no signs of infection i'm just curious and a bit worried! thanks:)))