Over the course of a full year, the daylight in a certain city follows a periodic pattern. The graph below represents the average daylight, in minutes, over the course of twenty-four months, with time t, representing the number of months after January 1 of a certain year. (5.5, 882), (11.5, 563), (17.5, 882), (23.5, 563)
What is the amplitude and what does it represent in this context?
To find the amplitude of the periodic pattern, we need to identify the highest point and the lowest point on the graph.
From the given information, we can see that the highest point on the graph is (5.5, 882), and the lowest point is (11.5, 563).
The amplitude of the periodic pattern is the difference between these two points in the y-coordinate. So, the amplitude is 882 - 563 = 319.
In this context, the amplitude represents the difference between the maximum and minimum amount of daylight in the city over the course of the year.