Questions: What is the average rate of change of the percentage of new employees from 2000 to 2006? % per year (Type an integer or a decimal rounded to two decimal places as needed.) What is the average rate of change of the percentage of new employees from 1994 to 2006? % per year (Type an integer or a decimal rounded to two decimal places as needed.)

Solution Steps

To find the average rate of change of the percentage of new employees over a given period, we need to use the formula for the average rate of change, which is:

\[ \text{Average Rate of Change} = \frac{\text{Percentage at End Year} - \text{Percentage at Start Year}}{\text{End Year} - \text{Start Year}} \]

We will apply this formula to the given periods: 2000 to 2006 and 1994 to 2006.

To find the average rate of change of the percentage of new employees from 2000 to 2006, we use the formula:

\[ \text{Average Rate of Change} = \frac{\text{Percentage at End Year} - \text{Percentage at Start Year}}{\text{End Year} - \text{Start Year}} \]

Given: \[ \text{Percentage at 2000} = 10.0\% \] \[ \text{Percentage at 2006} = 15.0\% \] \[ \text{Start Year} = 2000 \] \[ \text{End Year} = 2006 \]

Substitute the values into the formula:

\[ \text{Average Rate of Change} = \frac{15.0 - 10.0}{2006 - 2000} = \frac{5.0}{6} \approx 0.8333 \]

To find the average rate of change of the percentage of new employees from 1994 to 2006, we use the same formula:

Given: \[ \text{Percentage at 1994} = 8.0\% \] \[ \text{Percentage at 2006} = 15.0\% \] \[ \text{Start Year} = 1994 \] \[ \text{End Year} = 2006 \]

Substitute the values into the formula:

\[ \text{Average Rate of Change} = \frac{15.0 - 8.0}{2006 - 1994} = \frac{7.0}{12} \approx 0.5833 \]

Final Answer