Question

sea levels follow a periodic pattern of rise and fall called the tides. the graph below shows the sea level at a certain beach, in feet, over one day, where time t is measured in hours after 12:00 a.m. (midnight) on the first day. what is the period and what does it represent in this context?
sea level (in feet)
time (in hours)

Explanation:

Step1: Identify period - definition

The period of a periodic function is the smallest positive value of \(T\) such that \(f(t + T)=f(t)\) for all \(t\) in the domain of \(f\). In a graph of a periodic function, it is the horizontal distance between two consecutive points with the same value and slope.

Step2: Analyze the graph

Looking at the given graph of sea - level vs time, we can see that the pattern repeats. The sea - level values start to repeat after a certain time interval. We can take two consecutive points with the same characteristics. For example, consider the points \((1.5,0)\) and \((13.5,0)\).

Step3: Calculate the period

The time difference between these two points gives the period. We calculate the period \(T\) as \(T=13.5 - 1.5\).
\[T = 12\]

In the context of tides, the period represents the time interval between two consecutive high - tides or two consecutive low - tides.

Answer:

The period is 12 hours. It represents the time interval between two consecutive high - tides or two consecutive low - tides.