iPad 947 PM 9496 17 12 points AufCAT8 57065 My Notes Ask You

iPad 9:47 PM 9496. 17. -12 points AufCAT8 5.7.065 My Notes Ask Your Teacher During a 24-hour day, the tides raise and lower the depth of water at a pier as shown in the figure below. Write an equation of the form f(t)- A cos Bt +d that gives the depth of the water at time t. /(t) = Find the depth of the water at 12 A.M ft fu 12 12 18 24 t is the number of hours from 6 AM. Need Help? Read It Watch It Talk to a Tutor Submit Assignment Save Assignment Progress Home My Assignments Extension Request

Solution

from the graph amplitude is 3 . Hence A= 3

Now the graph shift upward by 9 units from the initial of 3 units. Hence d= 9

now we know that period = 2pi/B => 4pi= 2pi/B => B = 1/2

Hence equation is f(t) = 3cos(t/2) +9

Now from the graph we can see that at t= 12 we have depth = 12 feet. However, if we want to find it by the equation we got then f

f(12) = 3cos(12/2) +9 = 3cos6+9 = 11.9835 which is approximately equals 12 feet