Question

population density the table shows the population density for the state of texas in various years. find the average annual rate of change in the population density from 2000 to 2009.

| population density |

year	people per square mile
1930	22.1
1960	36.4
1980	54.3
2000	79.6
2009	96.7

source: bureau of the census, u.s. dept. of commerce

the population density increased by about \boxed{} people per square mile.

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Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change of a quantity \( y \) with respect to time \( t \) is \( \frac{\Delta y}{\Delta t}=\frac{y_2 - y_1}{t_2 - t_1} \), where \( y_1,y_2 \) are the initial and final values of the quantity and \( t_1,t_2 \) are the initial and final times.

Step2: Identify the values for 2000 and 2009

For \( t_1 = 2000 \), \( y_1=79.6 \) (people per square mile) and for \( t_2 = 2009 \), \( y_2 = 96.7 \) (people per square mile). The time difference \( \Delta t=t_2 - t_1=2009 - 2000 = 9 \) years. The change in population density \( \Delta y=y_2 - y_1=96.7 - 79.6=17.1 \) people per square mile.

Step3: Calculate the average annual rate of change

Using the formula \( \frac{\Delta y}{\Delta t} \), we substitute the values: \( \frac{17.1}{9}=1.9 \)

Answer:

\( 1.9 \)