https://file.aiquickdraw.com/mathbot/file/17260632060348ravn4gk.jpg

Let's analyze the graph and solve the questions based on the provided image.

### Overview of the Graph:
The graph shows the dive patterns of a sperm whale over a period of time, with depth (in meters) on the vertical axis and time (in minutes) on the horizontal axis. The blue line represents the depth of the whale at different points in time.

### Given Tasks:

#### a) **Determine the deepest depth reached by the whale.**
- By observing the graph, the deepest depth occurs at around -1500 meters (since the depth is given in negative values, representing the distance below the surface). 
- So, the deepest depth the whale reaches is approximately **1500 meters**.

#### b) **Determine the total time the whale spent deeper than 500 meters.**
- The whale dives below -500 meters on multiple occasions.
- The periods of deep dives (>500 meters) occur between:
  - From 0 to about 60 minutes.
  - From 180 to 240 minutes.
- The first dive lasts about **60 minutes** (from 0 to 60).
- The second dive lasts about **60 minutes** (from 180 to 240).
- Therefore, the whale spent a total of **120 minutes** below 500 meters.

#### c) **Classify the whale’s dives into deep dives (more than 500 meters) and shallow dives (less than 500 meters). Then calculate the average depth for both types of dives.**
- Based on the graph:
  - Deep dives (more than 500 meters) are marked as the segments below -500 meters.
  - Shallow dives (less than 500 meters) are segments where the whale stays between the surface and -500 meters.

For the average depth calculation:
1. Deep dives: The whale spends a significant portion of its time around -1500 meters during deep dives.
2. Shallow dives: The whale oscillates between the surface and -500 meters, often around -100 meters.

Let me know if you'd like a more detailed calculation or have further questions. Here are some follow-up questions:

### Follow-up questions:
1. What is the total duration of the whale's shallow dives?
2. Can you estimate the frequency of the whale's dives below 1000 meters?
3. How does the whale’s dive behavior change over the course of the time period?
4. What could be the biological or environmental reasons for the whale's deep dives?
5. Can the data be used to predict future diving patterns of the whale?

### Tip:
When analyzing dive patterns like this, it's useful to categorize depth ranges to gain insights into the whale's behavior and environment interactions.

The diagram shows the diving patterns of a sperm whale over a long period. The task is to analyze the graph and answer three questions: (a) determine the deepest depth reached by the whale, (b) calculate how long the whale was deeper than 500 meters, and (c) distinguish between deep dives (below 500 meters) and shallow dives (above 500 meters) and find the average depth for both types.

Learn how to analyze a graph showing a sperm whale's diving patterns. This problem focuses on determining the deepest depth reached, calculating the total time spent below 500 meters, and classifying dives into deep and shallow categories. Suitable for students in Grades 8-10.

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