the table below gives the annual sales (in millions) of a product.\n| year | 1998 | 1999 | 2000 | 2001 |…

the table below gives the annual sales (in millions) of a product.\n| year | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 |\n| sales | 274 | 292 | 306 | 316 | 322 | 324 | 322 | 316 | 306 |\nwhat was the average rate of change of annual sales\na) between 2000 and 2001\nmillions of dollars/year\nb) between 2000 and 2006\nmillions of dollars/year\nquestion help: message instructor\nsubmit question jump to answer

the table below gives the annual sales (in millions) of a product.\n| year | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 |\n| sales | 274 | 292 | 306 | 316 | 322 | 324 | 322 | 316 | 306 |\nwhat was the average rate of change of annual sales\na) between 2000 and 2001\nmillions of dollars/year\nb) between 2000 and 2006\nmillions of dollars/year\nquestion help: message instructor\nsubmit question jump to answer

Answer

Explanation:

Step1: Recall average rate - of - change formula

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, $x$ is the year and $y$ is the sales.

Step2: Calculate for the interval 2000 - 2001

In 2000, sales $f(2000)=306$ (in millions) and in 2001, sales $f(2001)=316$ (in millions). Using the formula $\frac{f(2001)-f(2000)}{2001 - 2000}=\frac{316 - 306}{1}=10$.

Step3: Calculate for the interval 2000 - 2006

In 2000, sales $f(2000)=306$ (in millions) and in 2006, sales $f(2006)=306$ (in millions). Using the formula $\frac{f(2006)-f(2000)}{2006 - 2000}=\frac{306 - 306}{6}=0$.

Answer:

a) 10 b) 0