Question

use the graph to estimate the average rate of change of the percentage of new employees from 1994 to 2000, from 2000 to 2006, and from 1994 to 2006

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

Explanation:

To solve for the average rate of change, we use the formula for average rate of change: $\text{Average Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$, where $x_1$ and $x_2$ are the input values (years), and $f(x_1)$ and $f(x_2)$ are the corresponding output values (percentage of new employees).

Step 1: Average Rate of Change from 1994 to 2000

• Let $x_1 = 1994$ and $x_2 = 2000$. From the graph, estimate $f(1994) \approx 0$ (at year 1994, the percentage is near 0) and $f(2000) \approx 18$ (at year 2000, the percentage is around 18).
• Calculate $\Delta x = 2000 - 1994 = 6$ years.
• Calculate $\Delta y = f(2000) - f(1994) \approx 18 - 0 = 18$.
• Average rate of change: $\frac{18}{6} = 3$ % per year.

Step 2: Average Rate of Change from 2000 to 2006

• Let $x_1 = 2000$ and $x_2 = 2006$. From the graph, $f(2000) \approx 18$ and $f(2006) \approx 22$ (at year 2006, the percentage is around 22).
• Calculate $\Delta x = 2006 - 2000 = 6$ years.
• Calculate $\Delta y = f(2006) - f(2000) \approx 22 - 18 = 4$.
• Average rate of change: $\frac{4}{6} \approx 0.67$ % per year (rounded to two decimal places).

Step 3: Average Rate of Change from 1994 to 2006

• Let $x_1 = 1994$ and $x_2 = 2006$. $f(1994) \approx 0$ and $f(2006) \approx 22$.
• Calculate $\Delta x = 2006 - 1994 = 12$ years.
• Calculate $\Delta y = 22 - 0 = 22$.
• Average rate of change: $\frac{22}{12} \approx 1.83$ % per year (rounded to two decimal places).

Final Answers:

• From 1994 to 2000: $\boldsymbol{3}$ % per year.
• From 2000 to 2006: $\boldsymbol{0.67}$ % per year (or similar, depending on graph precision).
• From 1994 to 2006: $\boldsymbol{1.83}$ % per year (or similar, depending on graph precision).

Answer:

To solve for the average rate of change, we use the formula for average rate of change: $\text{Average Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$, where $x_1$ and $x_2$ are the input values (years), and $f(x_1)$ and $f(x_2)$ are the corresponding output values (percentage of new employees).

Step 1: Average Rate of Change from 1994 to 2000

• Let $x_1 = 1994$ and $x_2 = 2000$. From the graph, estimate $f(1994) \approx 0$ (at year 1994, the percentage is near 0) and $f(2000) \approx 18$ (at year 2000, the percentage is around 18).
• Calculate $\Delta x = 2000 - 1994 = 6$ years.
• Calculate $\Delta y = f(2000) - f(1994) \approx 18 - 0 = 18$.
• Average rate of change: $\frac{18}{6} = 3$ % per year.

Step 2: Average Rate of Change from 2000 to 2006

• Let $x_1 = 2000$ and $x_2 = 2006$. From the graph, $f(2000) \approx 18$ and $f(2006) \approx 22$ (at year 2006, the percentage is around 22).
• Calculate $\Delta x = 2006 - 2000 = 6$ years.
• Calculate $\Delta y = f(2006) - f(2000) \approx 22 - 18 = 4$.
• Average rate of change: $\frac{4}{6} \approx 0.67$ % per year (rounded to two decimal places).

Step 3: Average Rate of Change from 1994 to 2006

• Let $x_1 = 1994$ and $x_2 = 2006$. $f(1994) \approx 0$ and $f(2006) \approx 22$.
• Calculate $\Delta x = 2006 - 1994 = 12$ years.
• Calculate $\Delta y = 22 - 0 = 22$.
• Average rate of change: $\frac{22}{12} \approx 1.83$ % per year (rounded to two decimal places).

Final Answers:

• From 1994 to 2000: $\boldsymbol{3}$ % per year.
• From 2000 to 2006: $\boldsymbol{0.67}$ % per year (or similar, depending on graph precision).
• From 1994 to 2006: $\boldsymbol{1.83}$ % per year (or similar, depending on graph precision).