To find the average rate of change of the function over the interval [tex]\( 18 \leq x \leq 24 \)[/tex], follow these steps:
1. Identify the given points on the interval:
- Let [tex]\( x_1 = 18 \)[/tex] and [tex]\( x_2 = 24 \)[/tex].
- The corresponding function values are [tex]\( f(x_1) = f(18) = 40 \)[/tex] and [tex]\( f(x_2) = f(24) = 39 \)[/tex].
2. Use the formula for the average rate of change:
[tex]\[
\text{Average rate of change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\][/tex]
3. Substitute the values into the formula:
[tex]\[
\text{Average rate of change} = \frac{f(24) - f(18)}{24 - 18} = \frac{39 - 40}{24 - 18}
\][/tex]
4. Perform the calculations:
[tex]\[
\text{Average rate of change} = \frac{39 - 40}{6} = \frac{-1}{6}
\][/tex]
Therefore, the average rate of change of the function over the interval [tex]\( 18 \leq x \leq 24 \)[/tex] is:
[tex]\[
-0.16666666666666666
\][/tex]
In simplest fractional form, this is [tex]\(-\frac{1}{6}\)[/tex].
