Question

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?
answer
attempt 1 out of 2
the period is
and it represents

Explanation:

Step1: Identify peak points

The first peak is at \( t = 2.5 \) hours and the next peak is at \( t = 14.5 \) hours.

Step2: Calculate the period

The period of a periodic function is the distance between consecutive peaks (or troughs). So, we subtract the two times: \( 14.5 - 2.5 = 12 \) hours.

Step3: Interpret the period

In the context of tides, the period represents the time it takes for the tide pattern (rise and fall) to repeat. So a period of 12 hours means the tide cycle (from one high tide to the next high tide, or one low tide to the next low tide) repeats every 12 hours.

Answer:

The period is \( 12 \) hours and it represents the time it takes for the tide pattern (rise and fall of sea level) to repeat.