# Salpeter Initial mass function

Barbequeman
Homework Statement:
A single stellar population is characterized by a single-slope initial mass function 𝜉(𝑀)=𝐴𝑀−(1+𝛽)across the mass interval 200Msun >= M >= 0.05Msun, which includes brown dwarfs.
(a) Calculate the constant A assuming a Salpeter IMF (i.e.  = 1.35) and that the total mass fraction between the two extremes is equal to 1.
(b) Which stellar mass corresponds to a 50 % mass fraction?
[ Hint: recall that 𝑀^−𝑥=𝐶 can be rearranged as 𝑀=𝐶^−1/𝑥.]
Relevant Equations:
Salpeter Mass Function
I calculated the following in the attached file, I hope I did it correctly...

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