Question

deling with periodic functions
test complete
2 3
what is the interpretation of the amplitude in this application?
the time between high tides
the time between high tide and low tide
the sum of the heights at high tide and low tide
the distance halfway between the height at high tide and low tide

Explanation:

1. Recall the definition of amplitude in a periodic function (like tidal height, a sinusoidal model): Amplitude is the maximum displacement from the midline (average value) of the function.
2. Analyze each option:

• "the time between high tides" is the period, not amplitude.
• "the time between high tide and low tide" is half - period (time to go from high to low), not amplitude.
• "the sum of the heights at high tide and low tide" is not related to amplitude (amplitude is a measure of deviation, not sum).
• "the distance halfway between the height at high tide and low tide": The midline (average of high and low tide heights) and amplitude is the distance from midline to high (or low) tide, which is the distance halfway between high and low tide heights (since midline is the average, amplitude is (high - low)/2, which is the distance from midline to either high or low, i.e., halfway between high and low in terms of distance from midline).

Answer:

the distance halfway between the height at high tide and low tide