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The initial mass function (IMF) of main-sequence stars, n(M) follows a shape called the Salpeter function,which is described by n(M)=kM^-2.35, where k is a normalising constant and M is the stellar mass in solar masses. The IMF is similar in some sense to a luminosity function except that mass is used instead of luminosity, i.e. it gives the number density of stars of a given mass per unit stellar mass. Given that the luminosity of a star depends on mass as L=M^4 (where L and M are given in Solar units), unse the IMF to derive an expression for the mass to light ratio M/L from main-sequence stars in the mass range M1 to M2, and use your fromula to estimate the mass-to-light ratio for a 10 Gyr-old main-sequence population covering a stellar mass range from 0.3-1 solar mass.

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# The initial mass function (IMF) of main-sequence stars,

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