On September 17, 2008, high tide in Portland was at midnight. The water level at high tide was 10.3 feet; later, at low tide, it was 0.3 feet. Assuming the next high tide is exactly at 12 noon and that the height of the water is given by a sine or cosine curve, find a formula for the water level in Portland as a function of time, where yy is the water level in feet, and tt is the time measured in hours from midnight.

Question

Mathematics

Alexus Nguyen

23 April, 06:17

On September 17, 2008, high tide in Portland was at midnight. The water level at high tide was 10.3 feet; later, at low tide, it was 0.3 feet. Assuming the next high tide is exactly at 12 noon and that the height of the water is given by a sine or cosine curve, find a formula for the water level in Portland as a function of time, where yy is the water level in feet, and tt is the time measured in hours from midnight.

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Brody Pham · Answer 1

Since at time 0 (midnight) the tide is at the highest, the tide is modeled by a cosine function.

The amplitude is

a = (10.3 - 0.3) / 2 = 5

The period is 12 hours

b = 2π / 12 = π/6

The vertical shift is

10.3 - 5 = 5.3

The equation then is

y = 5 cos (π/6 t) + 5.3