The figure shows the depth of water at the end of a boat doc

The figure shows the depth of water at the end of a boat dock. The depth is 3 feet at low tide and 9 feet at high tide. On a certain day. low tide occurs at 6 a m and high tide at noon. If y represents the depth of the water x hours after midnight, use a cosine function of the form y = A cosBx + D to model the water\'s depth. Write the equation for this problem in the form y = A cos Bx + D.

Solution

y = AcosBx +D

Amplitude A = 3 feet

Base = 6 as we can see it varied between 6+3, 6-3

So, D = 6

[pattern repeats after 18-6 = 12hrs

So, Period = 12hrs

B = 2pi/period = 2pi/12 = pi/6

y =3cos(pi*x/6) + 6