Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval (0leq xleq15).

Explanation:

Step1: Recall the formula for average rate of change

The formula for 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, \(a = 0\), \(b=15\), \(f(a)=f(0) = 9\), and \(f(b)=f(15)=159\).

Step2: Substitute the values into the formula

Substitute the values into the formula: \(\frac{f(15)-f(0)}{15 - 0}=\frac{159 - 9}{15}\).

Step3: Simplify the numerator

Simplify the numerator: \(159-9 = 150\). So the expression becomes \(\frac{150}{15}\).

Step4: Simplify the fraction

Simplify \(\frac{150}{15}\). Since \(150\div15 = 10\).

Answer:

\(10\)