Question

in response to rising concerns about identity theft, the number of models of paper shredders a company manufactures increased approximately steadily from 5 models in 1999 to 34 models in 2007. find the average rate of change of the number of shredder models manufactured per year between 1999 and 2007. the average rate of change of the number of paper shredders manufactured per year between 1999 and 2007 was \boxed{}. (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Identify the formula for average rate of change

The average rate of change formula is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $y_2,y_1$ are the final and initial values, and $x_2,x_1$ are the final and initial years.

Step2: Assign values

Let $x_1 = 1999$, $y_1 = 5$; $x_2 = 2007$, $y_2 = 34$.
Calculate $\Delta x=2007 - 1999 = 8$, $\Delta y=34 - 5 = 29$.

Step3: Compute the average rate of change

Using the formula, $\frac{\Delta y}{\Delta x}=\frac{29}{8}=3.625$. Rounded to two decimal places, it is $3.63$.

Answer:

3.63