https://file.aiquickdraw.com/mathbot/file/17303868111293n02sqvh.jpg

To find the rate of change of the airplane's elevation with respect to time, we need to determine the slope between two points in the table. The slope, or rate of change, can be calculated using the formula:

\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

where \( y \) represents elevation and \( x \) represents the number of minutes.

### Step-by-Step Calculation
Let's choose the first two points:
- Point 1: \( (2, 29000) \)
- Point 2: \( (4, 26000) \)

Using these points:
\[
\text{Slope} = \frac{26000 - 29000}{4 - 2} = \frac{-3000}{2} = -1500 \, \text{ft/min}
\]

The negative sign indicates a decrease in elevation over time, which is expected during descent.

### Answer
The rate of change is **1,500 ft/min**, so the correct answer is:
- **1,500 ft/min**

Would you like further details on this calculation or have additional questions?

### Related Questions
1. How would the rate of change differ if the airplane's ascent was shown instead of descent?
2. How can you interpret the significance of a negative slope in the context of this problem?
3. If given additional points, how could you confirm that the descent rate remains constant?
4. How would you calculate the descent time required to reach ground level at this rate?
5. How could you use this slope to find the equation of the line representing the airplane's descent?

### Tip
For linear relationships, the rate of change (slope) is constant across any two points on the line.

What is the rate of change of the elevation of the airplane with respect to the number of minutes since the plane started its descent?

Discover how to calculate the rate of descent of an airplane based on elevation and time data. This example uses the slope formula to find a constant descent rate of 1,500 ft/min, ideal for students learning about linear relationships and rate of change. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation