Question
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Find the average rate of change of \( g(x)=2 x+8 \) from \( x=6 \) to \( x=10 \). Simplify your answer as much as possible.

Ask by Hill Thornton. in the United States
Feb 03,2025

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Answer

The average rate of change is 2.

Solution

To find the average rate of change of the function \( g(x) = 2x + 8 \) from \( x = 6 \) to \( x = 10 \), you can use the following formula: \[ \text{Average rate of change} = \frac{g(b) - g(a)}{b - a} \] where \( a = 6 \) and \( b = 10 \). 1. **Calculate \( g(10) \):** \[ g(10) = 2(10) + 8 = 20 + 8 = 28 \] 2. **Calculate \( g(6) \):** \[ g(6) = 2(6) + 8 = 12 + 8 = 20 \] 3. **Compute the average rate of change:** \[ \text{Average rate of change} = \frac{28 - 20}{10 - 6} = \frac{8}{4} = 2 \] **Answer:** The average rate of change is \( 2 \).

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To find the average rate of change of the function \( g(x) = 2x + 8 \) from \( x = 6 \) to \( x = 10 \), we use the formula: \[ \text{Average Rate of Change} = \frac{g(b) - g(a)}{b - a} \] where \( a = 6 \) and \( b = 10 \). First, we evaluate \( g(6) \) and \( g(10) \): \[ g(6) = 2(6) + 8 = 12 + 8 = 20 \] \[ g(10) = 2(10) + 8 = 20 + 8 = 28 \] Now we can substitute these values into the average rate of change formula: \[ \text{Average Rate of Change} = \frac{g(10) - g(6)}{10 - 6} = \frac{28 - 20}{10 - 6} = \frac{8}{4} = 2 \] Thus, the average rate of change of \( g(x) \) from \( x=6 \) to \( x=10 \) is \( 2 \).

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