**Calculating the Average Rate of Change Over a Given Interval****Instructions:**Use the table below to calculate the average rate of change over the interval \(5 \leq x \leq 30\), rounded to three decimal places. You must show your work.| x | y ||----|---------|| 2 | 0 || 5 | 1.2619 || 10 | 2 || 15 | 2.4022 || 20 | 2.6801 || 25 | 2.8928 || 30 | 3.065 |**Solution:**To calculate the average rate of change of the function \( y \) with respect to \( x \) over the interval \( [5, 30] \):1. Identify the values of \( y \) corresponding to \( x = 5 \) and \( x = 30 \). \[ y_1 = 1.2619 \quad \text{(when } x = 5 \text{)}, \quad y_2 = 3.065 \quad \text{(when } x = 30 \text{)} \]2. Use the formula for the average rate of change: \[ \text{Average Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \]3. Substitute the values: \[ \text{Average Rate of Change} = \frac{3.065 - 1.2619}{30 - 5} = \frac{1.8031}{25} = 0.0721 \]Therefore, the average rate of change over the interval \(5 \leq x \leq 30\) is approximately \(0.072 \) (rounded to three decimal places).**Explanation of the Table:**The table shows two columns with values of \( x \) and corresponding values of \( y \). Each row represents a pair of \( x \) and \( y \) values which can be used to analyze the changes in \( y \) as \( x \) varies.- The first column represents the \( x \)-values: 2, 5, 10, 15, 20, 25, 30

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Use the table to calculate the average rage of change over the interval 5 ≤x≤ 30, rounded to 3 decimal places. You must show worki x y 20 5 1.2619 10 2 15 2.4022 20 2.6801 25 2.8928 30 3.065

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Calculating the Average Rate of Change Over a Given Interval**

**Instructions:**
Use the table below to calculate the average rate of change over the interval \(5 \leq x \leq 30\), rounded to three decimal places. You must show your work.

| x | y |
|----|---------|
| 2 | 0 |
| 5 | 1.2619 |
| 10 | 2 |
| 15 | 2.4022 |
| 20 | 2.6801 |
| 25 | 2.8928 |
| 30 | 3.065 |

**Solution:**
To calculate the average rate of change of the function \( y \) with respect to \( x \) over the interval \( [5, 30] \):

1. Identify the values of \( y \) corresponding to \( x = 5 \) and \( x = 30 \).
\[
y_1 = 1.2619 \quad \text{(when } x = 5 \text{)}, \quad y_2 = 3.065 \quad \text{(when } x = 30 \text{)}
\]

2. Use the formula for the average rate of change:
\[
\text{Average Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]

3. Substitute the values:
\[
\text{Average Rate of Change} = \frac{3.065 - 1.2619}{30 - 5} = \frac{1.8031}{25} = 0.0721
\]

Therefore, the average rate of change over the interval \(5 \leq x \leq 30\) is approximately \(0.072 \) (rounded to three decimal places).

**Explanation of the Table:**
The table shows two columns with values of \( x \) and corresponding values of \( y \). Each row represents a pair of \( x \) and \( y \) values which can be used to analyze the changes in \( y \) as \( x \) varies.

- The first column represents the \( x \)-values: 2, 5, 10, 15, 20, 25, 30

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