Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $18 \leq x \leq 24$.\
\

$x$	$f(x)$	\
-----	-------	\
12	41	\
18	40	\
24	39	\
30	38

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) over the interval \( [a, b] \) is given by \( \frac{f(b) - f(a)}{b - a} \).

Step2: Identify \( a \), \( b \), \( f(a) \), and \( f(b) \)

For the interval \( 18 \leq x \leq 24 \), we have \( a = 18 \), \( b = 24 \). From the table, \( f(18) = 40 \) and \( f(24) = 39 \).

Step3: Substitute into the formula

Substitute these values into the formula: \( \frac{f(24) - f(18)}{24 - 18} = \frac{39 - 40}{24 - 18} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( 39 - 40 = -1 \). Simplify the denominator: \( 24 - 18 = 6 \). So we have \( \frac{-1}{6} \).

Answer:

\( -\frac{1}{6} \)