QuestionTides in a specific location can be approximated using the periodic function shown on the graph.
What is the interpretation of the amplitude in this application?
Studdy Solution
STEP 1
What is this asking? What does the height difference between the highest and lowest tide tell us about the tides at this location? Watch out! Don't mix up the definitions of amplitude, period, and vertical shift!
STEP 2
1. Find the maximum and minimum tide heights.
2. Calculate the amplitude.
3. Interpret the amplitude.
STEP 3
Let's **carefully** examine the graph!
We see that the **highest** point the tide reaches is about meters.
This is our **maximum** tide height.
STEP 4
The **lowest** point the tide reaches is about meters.
This is our **minimum** tide height.
We've got our key values, nice!
STEP 5
Remember that the **amplitude** of a periodic function like this one is *half* the difference between the **maximum** and **minimum** values.
It's like finding the swing of the tide from its highest to its lowest point, and then cutting that swing in half!
STEP 6
So, let's **calculate** that **amplitude**! The **amplitude** is meters!
STEP 7
Now, what does this **amplitude** of meters *mean*?
It tells us how much the tide varies from the average tide height.
It's the height of the tide *above* or *below* the average water level.
STEP 8
Think of it like this: the average tide height is like the middle point of the tide's motion.
The amplitude tells us how far up *and* down the tide moves from that middle point.
STEP 9
The amplitude of meters represents the average height difference between the high and low tides.
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