Question

question 1
the table below gives the annual sales (in millions) of a product.
what was the average rate of change of annual sales
a) between 2000 and 2001
millions of dollars/year
b) between 2000 and 2003
millions of dollars/year

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 \([x_1,x_2]\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). Here, \(x\) represents the year and \(y\) represents the sales.

Step2: Calculate for part (a)

For the interval between \(2000\) (\(x_1 = 2000\), \(f(x_1)=307\)) and \(2001\) (\(x_2 = 2001\), \(f(x_2)=317\)):

$$
LATEXBLOCK0
$$

Step3: Calculate for part (b)

For the interval between \(2000\) (\(x_1 = 2000\), \(f(x_1)=307\)) and \(2003\) (\(x_2 = 2003\), \(f(x_2)=325\)):

$$
LATEXBLOCK1
$$

Answer:

a) \(10\) millions of dollars/year
b) \(6\) millions of dollars/year