https://file.aiquickdraw.com/mathbot/file/172607005505247eb4ofz.jpg

The graph shows three stages of a rocket's flight, with time in minutes on the x-axis and distance in miles on the y-axis. We need to find the average rate of change (essentially the slope) for each of the three intervals given.

### Let's solve for each stage:

1. **First stage: 0 to 2 minutes**
   - At 0 minutes, the rocket is at 0 miles.
   - At 2 minutes, the rocket is at 60 miles.
   
   Average rate of change = \(\frac{{\text{change in distance}}}{{\text{change in time}}} = \frac{{60 - 0}}{{2 - 0}} = \frac{60}{2} = 30 \, \text{mi/min}\).

2. **Second stage: 2 to 3 minutes**
   - At 2 minutes, the rocket is at 60 miles.
   - At 3 minutes, the rocket is at 120 miles.
   
   Average rate of change = \(\frac{{120 - 60}}{{3 - 2}} = \frac{60}{1} = 60 \, \text{mi/min}\).

3. **Third stage: 3 to 4 minutes**
   - At 3 minutes, the rocket is at 120 miles.
   - At 4 minutes, the rocket is at 300 miles.
   
   Average rate of change = \(\frac{{300 - 120}}{{4 - 3}} = \frac{180}{1} = 180 \, \text{mi/min}\).

### Summary of average rates of change:
- First stage: 30 mi/min
- Second stage: 60 mi/min
- Third stage: 180 mi/min

Would you like more details on how these calculations were done, or do you have any other questions? Here are some related questions to consider:

1. How do you find the rate of change for non-linear functions?
2. What does the slope represent in the context of this problem?
3. How would the graph change if the rocket decelerated?
4. What mathematical model could represent each segment of the graph?
5. How would you calculate the total distance traveled after 4 minutes?

**Tip:** Always label units clearly in word problems to avoid confusion during calculations.

What is the average rate of change over each interval in the rocket's flight? The graph shows three stages of the rocket's flight, with time on the x-axis and distance on the y-axis. The intervals are 0-2 minutes, 2-3 minutes, and 3-4 minutes.

This problem calculates the average rate of change in a rocket's flight over three intervals: 0-2 minutes, 2-3 minutes, and 3-4 minutes. The graph provided shows the distance traveled by the rocket in miles over time. Using basic rate of change and slope formulas, students can find how fast the rocket traveled in each interval.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation