At this one coastal city, the tides vary greatly during the day. During May, the predicted height of the tides are 3.0 m at 4 AM, 11 m at 10 AM, 3.0 m at 4 PM and 11 m at 10 PM. Assume we start the graph at midnight. What is the height of the tide at 7 AM? Round to the nearest tenth.
the average is (3+11)/2 = 7
the amplitude is (11-3)/2 = 4
the period is 24
h = average at t=4
so
h(t) = 7+4sin(π/12 (t-4))
so now find h(7)