Final answer:
Higher mass stars live shorter lives because they consume their fuel more rapidly than lower mass stars. The lifespan of a star on the main sequence is inversely proportional to its mass and rate of fuel consumption.
Step-by-step explanation:
The relationship between the mass of a star and its lifespan is such that higher mass stars live shorter lives than lower mass stars. Despite having more fuel, massive stars consume this fuel at a much faster rate, making their lifetimes much shorter. The lifespan of a star, referred to as 'T', can be expressed as T = 10ⁱ⁰ y, where 'M' represents the star's mass relative to the Sun's mass, and 'L' is its luminosity in comparison to the Sun.
This relationship is due to the fact that a star's lifetime on the main sequence is directly proportional to its mass and inversely proportional to its rate of fuel consumption (luminosity). Massive stars are significantly more luminous and hence exhaust their nuclear fuel more rapidly. A 1 solar mass star, for example, can spend roughly 10 billion years on the main sequence, whereas a star of 0.4 solar mass may remain in the main-sequence stage for about 200 billion years.