Question

question 13 · 1 point
given the table of values below, find the average rate of change of the function ( f(x) ) on the interval ( 7,14 ).

enter an exact answer.

provide your answer below:

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 7\) and \(b=14\).

Step2: Find \(f(a)\) and \(f(b)\) from the table

From the table, when \(x = 7\), \(f(7)=123\) (so \(f(a)=123\)), and when \(x = 14\), \(f(14)=251\) (so \(f(b)=251\)).

Step3: Substitute into the formula

Substitute \(a = 7\), \(b = 14\), \(f(a)=123\), and \(f(b)=251\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{251-123}{14 - 7}=\frac{128}{7}\approx18.29\).

Answer:

\(\frac{128}{7}\)