If luminosity is proportional to M^3.5, how does the main sequence lifespan ( au_MS) scale with mass (M)?
Answer
au_MS proportional M^{-2.5}
Since lifespan is inversely related to luminosity (the consumption rate) and directly related to available fuel (mass), the relationship simplifies to a sharp inverse correlation with mass raised to the power of 2.5.

Related Questions
What is the single most important factor determining a star's longevity?What physical state defines a star during its main sequence phase?What is the approximate mathematical relationship governing luminosity (L) based on a main-sequence star's mass (M)?If luminosity is proportional to M^3.5, how does the main sequence lifespan ( au_MS) scale with mass (M)?Which fusion process primarily powers stars significantly more massive than about 1.5 solar masses?What causes the extremely high luminosity and rapid fuel consumption in massive stars?What internal structure feature allows massive stars to utilize a larger fraction of their total hydrogen supply?What mechanism allows very low-mass red dwarfs (below 0.4 M_sun) to achieve lifespans potentially exceeding the current age of the universe?What element's formation in the core signals the end of energy generation for a massive star, triggering collapse?How does the post-main sequence evolution of a massive star differ from that of the Sun?