The life expectancy E of a main-sequence star depends on its mass M. The relation is given by the formula below where M is solar masses and E is solar lifetimes. E = M2.5 The sun is thought to be at the middle of its life, with a total life expectancy of about 10 billion years. Thus, the value E = 1 corresponds to a life expectancy of 10 billion years. (a) Does a more massive star have a longer or a shorter life expectancy than a less massive star? O longer Ⓒshorter (b) Spica is a main-sequence star that is about 7.3 solar masses. What is the life expectancy of Spica? (Round your answer to three decimal places.) 0.000602 x billion yr (c) Express using functional notation the life expectancy of a main-sequence star with mass equal to 3.5 solar mass. (Round your answers to one decimal place.) E 3.5 •) Calculate that valu 0.04363 x billion yr (d) Vega is a main-sequence star that is expected to live about 6.36 billion years. What is the mass of Vega? (Round your answer to two decimal places.) X solar masses (e) If one main-sequence star is three times as massive as another, how do their life expectancies compare? (Round your answer to two decimal places.) The life expectancy of the larger star is x times that of the smaller.

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