Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ( 0 leq x leq 4 ).

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\), \(b=4\), \(f(a)=f(0) = 3\), and \(f(b)=f(4)=48\).

Step2: Substitute the values into the formula

Substitute into \(\frac{f(b)-f(a)}{b - a}\), we get \(\frac{48 - 3}{4-0}\).

Step3: Simplify the expression

First, calculate the numerator \(48-3=45\), and the denominator \(4 - 0=4\). So the expression is \(\frac{45}{4}\).

Answer:

\(\frac{45}{4}\)