### Home > INT3 > Chapter 11 > Lesson 11.1.3 > Problem11-37

11-37.
1. Eliana is still working hard on her senior project. She has recorded the sunset time for at least one day a month through December. Her graph of the data is shown at right. Homework Help ✎

1. Write a function that models the time the sun sets as a function of the week #, where June 1 is Week 1.

2. What time should Eliana predict the sunset to take place during the first week of March (week 41)?

One possibility is to use cosine.

Find the variables for y = acosb(xc) + d.

$\text{Amplitude is }\frac{1}{2}(\text{max time}-\text{min time}).$

$\text{Week 4 to week 30 represents }\frac{1}{2} \text{ of the period.}$

$y=4\text{cos}\left(\frac{2\pi}{52}(x-4)\right)+7.7$

Substitute x = 41 into the answer from part (a).