Suppose that the length of time between consecutive high tid

Suppose that the length of time between consecutive high tides is approximately 12 5 hours. According to the National Oceanic and Atmospheric Administration, on a particular day in a city in Georgia, high tide occurred at 3.33 AM (3, 5500 hours) and low tide occurred at 9:48 AM (9, 8000 hours). Water heights are measured as the amounts above or below the mean lower tow water the height of the water at high tide was 8.2 feet and the height, of the water at low tide was - 0.8 foot. Answer the following Questions Approximately when will the next high tide occur? PM (Round to the nearest minute as needed) Find a sinusoidal function of the form y = A sin (omega x - Phi) + B that fits the data. A= omega = (Simplify your answer. Type an exact answer in terms of pi. Use integers or fractions for any numbers in the expression.) Phi (Round to four decimal places as needed.) B = Draw a graph of the function found in part (b). Which graph corresponds to the function? Use the function found in pal (b) to predict the height of the water at the next high tide. y feet (Round to one decimal place as needed.)

Solution

1) 1st high tide occured at t =3.55 hrs , next high tide = 3.55 +12.5 = 16.05 hrs = 4:03 pm

2) high tide = 8.2 ft ; low tide = -0.8 ft

base line = 3.7 , amplitude = 4.5 ft

period = 12.5 hrs ; w= 2pi/12.5

y = a*sin(2pi*x/12.5 - phi) + 3.7

at x = 3.55 hrs ; y = 8.2 ft

8.2 = 4.5sin(2pi*3.55/12.5 - phi) +3.7 ; sin(0.568pi - phi) = 1

phi = - 0.068pi

y = a*sin(2pi*x/12.5 +0.068pi) + 3.7

Graph : Option B

So, y = 4.5sin(