Questions: year 1998 1999 2000 2001 2002 2003 2004 2005 2006 sales 299 326 347 362 371 374 371 362 347. What was the average rate of change of annual sales a) Between 2001 and 2002 millions of dollars/year b) Between 2001 and 2006 millions of dollars/year

year  1998  1999  2000  2001  2002  2003  2004  2005  2006
sales  299  326  347  362  371  374  371  362  347.

What was the average rate of change of annual sales
a) Between 2001 and 2002 millions of dollars/year
b) Between 2001 and 2006 millions of dollars/year
Transcript text: \begin{tabular}{|l|r|r|r|r|r|r|r|r|r|} \hline year & 1998 & 1999 & 2000 & 2001 & 2002 & 2003 & 2004 & 2005 & 2006 \\ \hline sales & 299 & 326 & 347 & 362 & 371 & 374 & 371 & 362 & 347. \\ \hline \end{tabular} What was the average rate of change of annual sales a) Between 2001 and 2002 $\square$ millions of dollars/year b) Between 2001 and 2006 $\square$ millions of dollars/year
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Solution

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Solution Steps

Step 1: Identify the sales values for the relevant years

From the table, the sales values are:

  • 2001: 362 million dollars
  • 2002: 371 million dollars
  • 2006: 347 million dollars
Step 2: Calculate the average rate of change between 2001 and 2002

The average rate of change is calculated using the formula: \[ \text{Average rate of change} = \frac{\text{Change in sales}}{\text{Change in time}} \] For 2001 to 2002: \[ \text{Average rate of change} = \frac{371 - 362}{2002 - 2001} = \frac{9}{1} = 9 \] The average rate of change between 2001 and 2002 is \(\boxed{9}\) millions of dollars/year.

Step 3: Calculate the average rate of change between 2001 and 2006

For 2001 to 2006: \[ \text{Average rate of change} = \frac{347 - 362}{2006 - 2001} = \frac{-15}{5} = -3 \] The average rate of change between 2001 and 2006 is \(\boxed{-3}\) millions of dollars/year.

Final Answer

  • a) The average rate of change between 2001 and 2002 is \(\boxed{9}\) millions of dollars/year.
  • b) The average rate of change between 2001 and 2006 is \(\boxed{-3}\) millions of dollars/year.
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