Question 1198270: Weather Service releases weather balloons twice daily at over 90 locations in the United States in order to collect data for meteorologists. The height h (in feet) of a balloon is a function of the time t (in seconds) after the balloon is released, as shown.
a. Making a Table Make a table showing the height of
a balloon after t seconds for t = 0 through t = 10.
b. Drawing a Graph A balloon bursts after a flight of about 7200 seconds. Graph the function and identify the domain and range.
Answer by proyaop(69)   (Show Source):
You can put this solution on YOUR website! **a. Making a Table**
Unfortunately, I cannot provide the exact height function (h(t)) for a weather balloon. The ascent rate varies depending on factors like balloon size, weight of the payload, atmospheric conditions (temperature, pressure, wind), and the type of gas used to inflate the balloon.
However, I can provide a hypothetical example of a simplified height function and create a table based on that:
**Simplified Height Function (Example):**
* Let's assume the balloon ascends at a constant rate of 5 meters per second.
* h(t) = 5t
**Table of Heights (Example):**
| Time (t) (seconds) | Height (h) (meters) |
|---|---|
| 0 | 0 |
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
| 5 | 25 |
| 6 | 30 |
| 7 | 35 |
| 8 | 40 |
| 9 | 45 |
| 10 | 50 |
**b. Drawing a Graph**
* **Based on the Example:**
* The graph of h(t) = 5t would be a straight line passing through the origin with a slope of 5.
* **Considering a Real-World Scenario:**
* The actual height of a weather balloon would likely not increase linearly. It would likely accelerate initially and then slow down as it reaches higher altitudes where the air density decreases.
* The graph would probably be a curve, possibly with an initial steeper slope and then gradually leveling off.
* **Domain and Range:**
* **Domain:**
* The domain represents the possible values for time (t).
* In this case, the domain is 0 ≤ t ≤ 7200 seconds (since the balloon bursts after 7200 seconds).
* **Range:**
* The range represents the possible values for height (h).
* In the simplified example, the range would depend on the maximum height reached.
**Important Notes:**
* This is a simplified example. The actual ascent rate of a weather balloon is much more complex.
* Weather balloon data is collected and analyzed by meteorological agencies. You can find more information and potentially access real-world data on their websites.
I hope this helps! Let me know if you have any further questions or would like to explore a more realistic height function.
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