I need help understanding initial mass function. In class the teacher gave us a example to understand this concept but I am completely lost. Can someone please decrypt this problem for me? I really don't have a clue on how to get started at all. Assume the milky way contains 5 x 10^10 Solar masses of gas and 10^11 stars that were formed with an initial mass function dN/dM α M^-2.35 in the range 0.4-100 solar masses. What fraction of stars formed with a mass above 8 Solar Masses,, the threshold for eventual core collapse? About how many neutron stars and black holes are there in the galaxy?