The water level at a local pier rises and falls with the tide. Yesterday, the maximum depth of the water at the pier was 8 feet, and the minimum depth was 4 feet. High tide occurred at 12:00 AM and low tide
occurred at 12:20 PM. Which function models the depth, in feet, of the water at the pier yesterday, as a
function of time t in minutes past high tide?

The function  is  

Step-by-step explanation:

From the question we are told that

    The  maximum depth is

      The  minimum depth is  

Generally the average depth is mathematically represented as

=>  

Generally  the amplitude is mathematically represented as

=>    

=>    

Generally the period is  24 hours given that the the interval between the maximum depth and the minimum depth is half a day

Generally the period is mathematically represented as

here w is the angular  frequency

So

Generally the depth can be modeled with a sin function as follows

Now  from co-function identity we have  that

So