Problem

The table below gives the annual sales (in millions of dollars) of a product.
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|}
\hline year & 1998 & 1999 & 2000 & 2001 & 2002 & 2003 & 2004 & 2005 & 2006 \\
\hline sales & 256 & 283 & 304 & 319 & 328 & 331 & 328 & 319 & 304 \\
\hline
\end{tabular}

Determining the average rate of change of sales is important. It tells whether sales are increasing or decreasing over a time period, and at what rate.
a) What was the average rate of change of annual sales between 2000 and 2001 ?
miltions of dollars/year
b) What was the average rate of change of annual sales between 2000 and 2004 ?
millions of dollars/year

Answer

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Answer

Final Answer: a) The average rate of change of annual sales between 2000 and 2001 is \(\boxed{15}\) millions of dollars/year. b) The average rate of change of annual sales between 2000 and 2004 is \(\boxed{6}\) millions of dollars/year.

Steps

Step 1 :The average rate of change is calculated by subtracting the initial value from the final value and then dividing by the change in time. In this case, the initial and final values are the sales in the initial and final years, and the change in time is the difference in years.

Step 2 :For part a), the initial year is 2000 and the final year is 2001. The sales in 2000 were 304 million dollars and the sales in 2001 were 319 million dollars. The change in time is 1 year.

Step 3 :Subtract the sales in 2000 from the sales in 2001 to get the change in sales: \(319 - 304 = 15\) million dollars.

Step 4 :Divide the change in sales by the change in time to get the average rate of change: \(\frac{15}{1} = 15\) million dollars/year.

Step 5 :For part b), the initial year is 2000 and the final year is 2004. The sales in 2000 were 304 million dollars and the sales in 2004 were 328 million dollars. The change in time is 4 years.

Step 6 :Subtract the sales in 2000 from the sales in 2004 to get the change in sales: \(328 - 304 = 24\) million dollars.

Step 7 :Divide the change in sales by the change in time to get the average rate of change: \(\frac{24}{4} = 6\) million dollars/year.

Step 8 :Final Answer: a) The average rate of change of annual sales between 2000 and 2001 is \(\boxed{15}\) millions of dollars/year. b) The average rate of change of annual sales between 2000 and 2004 is \(\boxed{6}\) millions of dollars/year.

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