the depth of the water at the end of a pier changes periodically along with the movement of tides. on a…

the depth of the water at the end of a pier changes periodically along with the movement of tides. on a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. let (t = 0) be 12:00 am. write a cosine model, (d=acos(bt)+k), for the depth as a function of time. the amplitude is meters. (a=)

the depth of the water at the end of a pier changes periodically along with the movement of tides. on a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. let (t = 0) be 12:00 am. write a cosine model, (d=acos(bt)+k), for the depth as a function of time. the amplitude is meters. (a=)

Answer

Explanation:

Step1: Find the amplitude formula

The amplitude $a$ of a periodic - function is given by $a=\frac{\text{max}-\text{min}}{2}$, where $\text{max}$ is the maximum value and $\text{min}$ is the minimum value of the function.

Step2: Identify maximum and minimum depths

The low - tide depth (minimum) is $2.5$ m and the high - tide depth (maximum) is $5.5$ m.

Step3: Calculate the amplitude

$a=\frac{5.5 - 2.5}{2}=\frac{3}{2}=1.5$

Answer:

$1.5$