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[2π365(t−80)]
We can check the model using March 31st, which is day 90 of the year:
$L(t)=12+2 sin[\frac{2\pi}{365}(t−80)]$
$L=12+2 sin[\frac{2\pi}{365}(t−80)]$
$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
