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, 893), (11.5, 484), (17.5, 893), (23.5, 484)
What is the amplitude and what does it represent in this context?
The amplitude of a periodic function represents the maximum deviation of the function from its average value. In this context, the average value of the daylight over the course of the year can be approximated as the average of the y-coordinates of the given points, which is (893 + 484 + 893 + 484)/4 = 688.5 minutes.
To find the amplitude, we need to find the maximum deviation from the average value. From the given points, we can see that the maximum y-coordinate is 893 and the minimum y-coordinate is 484. The maximum deviation from the average value is therefore (893 - 688.5) = 204.5 minutes.
Therefore, the amplitude is 204.5 minutes, which represents the maximum deviation from the average daylight over the course of the year in this city.