question 1\nthe table below gives the annual sales (in millions) of a product.\nwhat was the average rate of…

question 1\nthe table below gives the annual sales (in millions) of a product.\nwhat was the average rate of change of annual sales\na) between 2000 and 2001\nmillions of dollars/year\nb) between 2000 and 2003\nmillions of dollars/year

question 1\nthe table below gives the annual sales (in millions) of a product.\nwhat was the average rate of change of annual sales\na) between 2000 and 2001\nmillions of dollars/year\nb) between 2000 and 2003\nmillions of dollars/year

Answer

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)): [ \begin{align*} \frac{f(x_2)-f(x_1)}{x_2 - x_1}&=\frac{317 - 307}{2001-2000}\ &=\frac{10}{1}\ & = 10 \end{align*} ]

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)): [ \begin{align*} \frac{f(x_2)-f(x_1)}{x_2 - x_1}&=\frac{325-307}{2003 - 2000}\ &=\frac{18}{3}\ &=6 \end{align*} ]

Answer:

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