The Cobscook Bay tides vary between 4 feet and 20 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 18 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? Amplitude = 16 feet; period = 9 hours; midline: y = 8 Amplitude = 16 feet; period = 18 hours; midline: y = 12 Amplitude = 8 feet; period = 9 hours; midline: y = 8 Amplitude = 8 feet; period = 18 hours; midline: y = 12

Answer: Last OptionAmplitude = 8 feet; period = 18 hours; midline: y = 12Step-by-step explanation:This problem can be modeled by a sinusoidal function.By definition the amplitude of a periodic function is half the distance between the minimum value and the maximum value of the function.In this case we know that the minimum value is 4 and the maximum value is 20. Then the amplitude A is:[tex]A = 0.5 (20-4)[/tex][tex]A = 8\ ft[/tex]The middle line is a horizontal line that cuts the graph at its midpoint.The midline is calculated as:[tex]y = V_{max} - A[/tex]Where A is the amplitude and Vmax is the maximum value of the function[tex]y = 20-8[/tex][tex]y = 12[/tex]Finally, the period is the time it takes for the function to complete a cycle. In this case we know that it takes 18 hours. So the period is 18 hoursThe answer is: "Amplitude = 8 feet; period = 18 hours; midline: y = 12"