Question

a cepheid star is a type of variable star, which means that 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. use a calculator to solve each problem. round your answers to the nearest hundredth. what is the absolute magnitude of a star that has a period of 62 days? what is the absolute magnitude of a star that has a period of 50 days?

Explanation:

Step1: Calculate $\log(62)$

$\log(62) \approx 1.7924$

Step2: Substitute into the formula for $P=62$

$M = -2.78\times1.7924 - 1.35$
$M \approx -5.0829 - 1.35$
$M \approx -6.43$

Step3: Calculate $\log(50)$

$\log(50) \approx 1.6990$

Step4: Substitute into the formula for $P=50$

$M = -2.78\times1.6990 - 1.35$
$M \approx -4.7232 - 1.35$
$M \approx -6.07$

Answer:

For a period of 62 days: $-6.43$
For a period of 50 days: $-6.07$