Question

sales of a new product increase over time. the table shows the value of a function $f(x)$, which equals product sales, for the first 6 years of sales.
what is the average rate of change of the function from the year $x = 3$ to $x = 5$?
a 8
b 20
c 0
d 16

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 3\), \(b=5\), \(f(3)=14\), and \(f(5)=30\).

Step2: Substitute the values into the formula

Substitute the values into \(\frac{f(b)-f(a)}{b - a}\), we get \(\frac{30 - 14}{5-3}\).
First, calculate the numerator: \(30-14 = 16\).
Then, calculate the denominator: \(5 - 3=2\).
So, \(\frac{30 - 14}{5-3}=\frac{16}{2}\).

Step3: Simplify the fraction

Simplify \(\frac{16}{2}=8\).

Answer:

A. 8