Question

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. what is the amplitude and what does it represent in this context? (the graph has the vertical axis labeled average daylight (in minutes) with values from 100 to 900, and the horizontal axis labeled time (in months) with values from 0 to 24. points on the graph are (11.5, 858), (23.5, 858), (5.5, 523), (17.5, 523), and the curve starts at (0, around 850) and has a wavy pattern.) answer attempt 1 out of 2 the amplitude is \boxed{} and it represents

Explanation:

Step1: Find max and min values

Max daylight: $858$ minutes; Min daylight: $523$ minutes

Step2: Calculate amplitude

Amplitude = $\frac{\text{Max} - \text{Min}}{2} = \frac{858 - 523}{2}$

Step3: Compute the value

$\frac{858 - 523}{2} = \frac{335}{2} = 167.5$

Step4: Interpret the amplitude

It is half the total variation in daylight.

Answer:

The amplitude is $167.5$ minutes, and it represents half the difference between the maximum and minimum average daylight minutes over the year, or the maximum amount that the average daylight deviates from the yearly average daylight.