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

11-37.

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.

One possibility is to use cosine.

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

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

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

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

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

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