Question

A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by M = –2.78(log P) – 1.35, where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth.
–5.95
–4.60
3.25
4.60

Answer 1

M = −2.78 log(45) − 1.35.
log10(45) ≈ 1.65321, so M ≈ −2.78(1.65321) − 1.35 ≈ −4.59593 − 1.35 ≈ −5.94593.
Rounded to the nearest hundredth: −5.95.