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.

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

   Hint 1(a):

   One possibility is to use cosine.

   Hint 2(a):

   Find the variables for $y=a\cos b(x−c)+d$.

   Hint 3(a):

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

   Hint 4(a):

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

   Possible Answer (a):

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

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

   Hint (b):

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