Find the average rate of change of k(x)=10
x–8 over the interval [8,16].
Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions.

The average rate of change of a function over an interval \([a, b]\) is given by the formula:

\[
\frac{k(b) - k(a)}{b - a}
\]

The given function is \( k(x) = \frac{10}{x} - 8 \), and the interval is \([8, 16]\).

### Step 1: Find \( k(16) \)
\[
k(16) = \frac{10}{16} - 8 = 0.625 - 8 = -7.375
\]

### Step 2: Find \( k(8) \)
\[
k(8) = \frac{10}{8} - 8 = 1.25 - 8 = -6.75
\]

### Step 3: Calculate the average rate of change
Now, apply the formula for the average rate of change:

\[
\text{Average rate of change} = \frac{k(16) - k(8)}{16 - 8} = \frac{-7.375 - (-6.75)}{16 - 8} = \frac{-7.375 + 6.75}{8} = \frac{-0.625}{8} = -0.078125
\]

### Step 4: Round to the nearest tenth
The average rate of change rounded to the nearest tenth is:

\[
\boxed{-0.1}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the average rate of change for linear functions?
2. What is the interpretation of the average rate of change in real-world problems?
3. Can the average rate of change ever be zero? If so, when?
4. How does the average rate of change differ from the instantaneous rate of change?
5. How do you calculate the average rate of change for quadratic functions?

**Tip:** The average rate of change is essentially the slope of the secant line between two points on a function!

Find the average rate of change of k(x)=10/x–8 over the interval [8,16]. Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions.

Learn how to find the average rate of change of the function k(x) = 10/x - 8 over the interval [8, 16]. This step-by-step solution covers key algebraic concepts, including the formula for average rate of change and the interpretation of secant line slopes. Suitable for students in Grades 10-12.

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