Answer
$L(t) = 12+2~sin[\frac{2\pi}{365}(t-80)]$
Work Step by Step
We can see that the average number of hours is 12 hours and the amplitude of the graph is 2 hours.
We can write a function for the number of hours of sunlight:
$L(t) = 12+2~sin[\frac{2\pi}{365}(t-80)]$
We can check the model using March 31st, which is day 90 of the year:
$L(t) = 12+2~sin[\frac{2\pi}{365}(t-80)]$
$L = 12+2~sin[\frac{2\pi}{365}(90-80)]$
$L = 12.34~hours$
The data shows that the amount of sunlight on this day is $6:18~pm - 5:51~am$ which is $12~h~27~min$. Note that this is $12.45~hours$
