The water level varies from 12 inches at low tide to 64 inches at high tide. Low tide occurs at 8 am and high tide occurs at 1:30 pm. What is a cosine function that models the variation in inches above and below the water level as a function of time in hours since 8 am?(5 points)

Answer 1

Let's assume that the water level reaches its lowest point at x=0 (8 am) and its highest point at x=5.5 (1:30 pm).

A cosine function that models this variation is:

y = 26cos(2π/5.5(x-2.75)) + 38

Where:
- y represents the water level in inches above or below the average level (26 inches below and 26 inches above the average level).
- The period is 5.5 hours since the water level reaches its lowest point at x=0 and highest point at x=5.5.
- The amplitude is 26, half of the difference between the highest and lowest water levels.
- The average level is 38, the average between 12 inches at low tide and 64 inches at high tide.