Rosenthal stumbled onto David’s scorings on the wall, he wasn’t marking the days. He kept track of how long Elizabeth Shaw was kept alive using his experiments on her. Depending on the local year, 3,800 or so days is a very long time.
I have added the calculation assuming the local year is similar to that of Earth.
Other proposed alternatives are:
He knew the USCSS Covenant was coming.
He marked out a path for Elizabeth so she could get water, seeing as humans get lost easily.