Question
On Dolphin Beach, the high tide is 1.8 meters and only occurs at 12 a.m. and 12 p.m. The low tide is 0.4 meter and only occurs at 6 a.m. and 6 p.m.
Which function models the height of the tide t hours after 12 a.m.?
A possible function that models the height of the tide t hours after 12 a.m. is:
h(t) = 1.2sin(πt/6) + 0.7
This function takes into account the difference between high and low tides (1.8 - 0.4 = 1.4 meters), the midpoint between high and low tides (1.1 meters), and the timing of the tides (6-hour period between high and low tides).