Answer:
See below under "explanation".
General Formulas and Concepts:
Algebra I
Functions
Average Rate of Change Formula:
[tex]\displaystyle \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}[/tex]
- b is upper interval bound
- a is lower interval bound
Step-by-step explanation:
*Note:
The function is unclear, so I will provide 2 possible answers.
Step 1: Define
Identify given.
[tex]\displaystyle \begin{aligned}1. \ f(x) & = \sqrt{x} + 4 \\2. \ f(x) & = \sqrt{x + 4} \\\end{aligned}[/tex]
[tex]\displaystyle \text{Interval: } 2 \leq x \leq 6[/tex]
Step 2: Find Average Rate of Change
For the 1st function:
[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\big( \sqrt{b} + 4 \big) - \big( \sqrt{a} + 4 \big)}{b - a} \\& = \frac{\big( \sqrt{6} + 4 \big) - \big( \sqrt{2} + 4 \big)}{6 - 2} \\& = \frac{\sqrt{6} - \sqrt{2}}{4} \\& = 0.258819 \\& \approx \boxed{0.26} \\\end{aligned}[/tex]
∴ the average rate of change, if using the 1st defined function, will be approximately 0.26.
For the 2nd function:
[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\sqrt{b + 4} - \sqrt{a + 4} }{b - a} \\& = \frac{\sqrt{6 + 4} - \sqrt{2 + 4}}{6 - 2} \\& = \frac{\sqrt{10} - \sqrt{6}}{4} \\& = 0.178197 \\& \approx \boxed{0.18} \\\end{aligned}[/tex]
∴ the average rate of change, if using the 2nd defined function, will be approximately 0.18.
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Topic: Algebra I
