Assume a galaxy forms its stars in a single rapid burst, with aSalpeter initial mass function extending from 0.1 to 100 Msun.After 10 Gyrs have passed, divide the surviving stars into threegroups: lower main-sequence upper main sequence (MS stars with mass> 0.75 Msun), lower main sequence (MS stars with mass < 0.75Msun), and red giants. Calculate the fractional contribution ofeach group to: 

(a) the total number of surviving stars. (b) the total mass insurviving stars. (c) the total luminosity of the galaxy.
Hints: Assume the MS lifetime-vs-mass relation and RGB lifetimesas given in Lecture I. Ignore post-RGB evolutionary stages. For MSstars, assume luminosity-mass relation of (L/Lsun) = (M/Msun)3.5.Assume (crudely) that the average RGB luminosity is ~100 timeshigher than the turn-off luminosity. 

