Question

The water level in a lake rises and falls throughout the day. The average depth of the water at low tide is 4 metres, while the average depth at high tide is 8 metres. It takes 6 hours for the water level to rise from low tide to high tide.

a) Determine a cosine equation to model the water depth, assuming that at t = 0
hours the water is at low tide

b) What is the depth of the water 2 hours after low tide?

Answer 1

Amplitude is (max-min)/2 = (8-4)/2 = 2
middle line is (max+min)/2 = 6
the period is roughly 12 hours, so 2π/k = 12
So far, we have y = 6+2cos(π/6x)
Since cos(x) is max at t=0, and we want it to be a min, make that
y = 6-2cos(π/6 x)

Now plug in x=2