Along with other graphs, we were asked to estimate the age of the cluster. Our professor chose the turn off point marked on the graph and worked out the temperature of the stars there and then with another graph related it to the average mass of star at that point. Then using an equation we were given which gives a rough relation between the time a star spends on the main sequence and its mass, an average time in the main sequence of 5.3 Gy was found for such stars.
He then said that, since they are about to finish their main sequence lives, this time is a valid estimate for the life time of the star cluster.
My question is that how do we know that they are at the end of their lives? All I can tell is that a star at that marked point will have a main sequence life time of about 5.3 Gy, I see no obvious reason to believe the star is at the end of its main sequence. My only guess is the fact that its located at the sharp bend.
Can anyone explain my professors explanation for why the ms life time of a star at that point is a valid approximation for the clusters lifetime?