The functionthat defines the brightness of the star Delta Cephei in terms of time.

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.3, Problem 26E
To determine

To find: The functionthat defines the brightness of the star Delta Cephei in terms of time.

Expert Solution

The brightness of Delta Cephei is given by the function M(t)=4.0+0.35sin(2π5.4t) .

Explanation of Solution

Given:

Time period of the maximum brightness of the star Delta Cephei is 5.4 days with the average brightness 4.0 and it varies by ±0.35 .

Calculation:

As the maximum period of brightness is 5.4 days consider total time period for Delta Cephei as 5.4 days.

Since the time period is of 5.4 days, the time period in terms of time t is given by sin(2π5.4t) .

Note that the average amplitude of the star is 4.0 with variation of ±0.35 in the magnitude.

Use the above information to construct a function to calculate the brightness of the starDelta Cephei as shown below,

M(t)=4.0+0.35sin(2π5.4t) .

Therefore, the function that models the brightness of star in Delta Cephei as function of time is M(t)=4.0+0.35sin(2π5.4t) .

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