How does the main sequence lifetime ($ au$) scale inversely with initial stellar mass (M), based on the given relationships?
Answer
$$\tau \propto 1/M^{2.5}$$
By substituting the mass-luminosity relation ($L \propto M^{3.5}$) into the lifespan ratio ($\text{Lifetime} \propto M/L$), the resulting relationship shows that lifespan scales inversely with mass raised to the power of 2.5.
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