Answer:
- L(t) = 727.775 -51.875cos(2π(t +11)/365)
- 705.93 minutes
Step-by-step explanation:
a) The midline of the function is the average of the peak values:
(675.85 +779.60)/2 = 727.725 . . . minutes
The amplitude of the function is half the difference of the peak values:
(779.60 -675.85)/2 = 51.875 . . . minutes
Since the minimum of the function is closest to the origin, we choose to use the negative cosine function as the parent function.
Where t is the number of days from 1 January, we want to shift the graph 11 units to the left, so we will use (t+11) in our function definition.
Since the period is 365 days, we will use (2π/365) as the scale factor for the argument of the cosine function.
Our formula is ...
L(t) = 727.775 -51.875cos(2π(t +11)/365)
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b) L(55) ≈ 705.93 minutes
