The function f(t) = 5 cos(pi over 6t) + 7 represents the tide in Stanley Sea. It has a maximum of 12 feet when time (t) is 0 and a minimum of 2 feet. The sea repeats this cycle every 12 hours. After four hours, how high is the tide? 11.3 feet 9.5 feet 4.5 feet 2.6 feet

The function for the height is
[tex]f(t) = 5cos( \frac{ \pi }{6} t)+7[/tex]

f(0) = 5 cos(0) + 7 = 5 + 7 = 12  (verified)
The period is T  = 12 hours.

After 4 hours (t = 4), the height is
[tex]f(4) = 5cos( \frac{ 4\pi }{6} )+7 = 5*(-0.5)+7=4.5[/tex]

A graph of f(t) confirms the answer.

Answer: 4.5 ft