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 ≤ x ≤ 15.

x	f(x)
3	39
6	69
9	99
12	129
15	159

Explanation:

Step1: Identify interval endpoints

From the table, at \(x=0\), \(f(0)=9\); at \(x=15\), \(f(15)=159\).

Step2: Apply average rate formula

Average rate = \(\frac{f(b)-f(a)}{b-a}\) where \(a=0\), \(b=15\).

Step3: Calculate numerator and denominator

Numerator: \(159 - 9 = 150\); Denominator: \(15 - 0 = 15\).

Step4: Simplify the ratio

\(\frac{150}{15} = 10\).

Answer:

10