The Depth of Water $d ( t )$ At My Favorite Surfing Spot Varies from 8 to 20

Multiple Choice

The depth of water $d ( t )$ at my favorite surfing spot varies from 8 to 20 feet, depending on the time. Last Sunday high tide occurred at 5:00 A.M. and the next high tide occurred at 6:30 P.M. Use a sine function to model the depth of water as a function of time t in hours since midnight on Sunday morning.

A) $d ( t ) = 10 \sin \left( \frac { 2 \pi ( t - 1.625 ) } { 13.5 } \right) + 4$
B) $d ( t ) = 6 \sin \left( \frac { 2 \pi ( t + 1.625 ) } { 11.5 } \right) - 14$
C) $d ( t ) = - 6 \sin \left( \frac { - 2 \pi ( t + 1.625 ) } { 13.5 } \right) + 14$
D) $d ( t ) = 6 \sin \left( \frac { 2 \pi ( t - 1.625 ) } { 13.5 } \right) + 14$
E) $d ( t ) = 14 \sin \left( \frac { 2 \pi ( t - 1.625 ) } { 13.5 } \right) + 6$