Questions: year 1998 1999 2000 2001 2002 2003 2004 2005 2006 sales 107 125 139 149 155 157 155 149 139 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 1998 and 1999? millions of dollars/year b) What was the average rate of change of annual sales between 1998 and 2000? millions of dollars/year Give your answers as whole numbers.

year  1998  1999  2000  2001  2002  2003  2004  2005  2006
sales  107  125  139  149  155  157  155  149  139

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 1998 and 1999? millions of dollars/year
b) What was the average rate of change of annual sales between 1998 and 2000? millions of dollars/year

Give your answers as whole numbers.
Transcript text: \begin{tabular}{|c|r|r|r|r|r|r|r|r|r|} \hline year & 1998 & 1999 & 2000 & 2001 & 2002 & 2003 & 2004 & 2005 & 2006 \\ \hline sales & 107 & 125 & 139 & 149 & 155 & 157 & 155 & 149 & 139 \\ \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 1998 and 1999? $\square$ millions of dollars/year b) What was the average rate of change of annual sales between 1998 and 2000? $\square$ millions of dollars/year Give your answers as whole numbers.
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Solution

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Solution Steps

Step 1: Identify the Sales in the Initial and Final Years

The sales in the initial year, \(S_i\), is 107. The sales in the final year, \(S_f\), is 125.

Step 2: Calculate the Difference in Sales

The difference in sales, \(\Delta S\), is calculated as \(\Delta S = S_f - S_i = 125 - 107 = 18\).

Step 3: Calculate the Number of Years Over the Period

The number of years, \(\Delta Y\), over the period is calculated as \(\Delta Y = Y_f - Y_i = 1999 - 1998 = 1\).

Step 4: Compute the Average Rate of Change of Annual Sales

The average rate of change of annual sales, \(R\), is calculated as \(R = \frac{\Delta S}{\Delta Y} = \frac{18}{1} = 18\).

Final Answer:

The average rate of change of annual sales over the period from 1998 to 1999 is approximately 18 sales units per year, rounded to 0 decimal places.

Step 1: Identify the Sales in the Initial and Final Years

The sales in the initial year, \(S_i\), is 107. The sales in the final year, \(S_f\), is 139.

Step 2: Calculate the Difference in Sales

The difference in sales, \(\Delta S\), is calculated as \(\Delta S = S_f - S_i = 139 - 107 = 32\).

Step 3: Calculate the Number of Years Over the Period

The number of years, \(\Delta Y\), over the period is calculated as \(\Delta Y = Y_f - Y_i = 2000 - 1998 = 2\).

Step 4: Compute the Average Rate of Change of Annual Sales

The average rate of change of annual sales, \(R\), is calculated as \(R = \frac{\Delta S}{\Delta Y} = \frac{32}{2} = 16\).

Final Answer:

The average rate of change of annual sales over the period from 1998 to 2000 is approximately 16 sales units per year, rounded to 0 decimal places.

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