Question

directions: read the scenario below and solve. show your work. the graph below represents the number of producing gas wells in kansas from 1989 to 2017. what is the average rate change between 2000 and 2015? number of producing gas wells count 30,000 (2015, 24,468) 25,000 (1995, 22,020) (2005, 18,946) (2010, 22,145) 20,000 15,000 (1990, 16,980) (2000, 15,206) 10,000 5,000 0 1990 1995 2000 2005 2010 2015 — kansas natural gas number of gas and gas condensate wells source: u.s. energy information administration

Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x$ represents the year and $y$ represents the number of producing gas - wells. Let $x_1 = 2000$, $y_1=15206$, $x_2 = 2015$, and $y_2 = 24468$.

Step2: Substitute values into the formula

$\frac{y_2 - y_1}{x_2 - x_1}=\frac{24468 - 15206}{2015 - 2000}$.

Step3: Calculate the numerator and denominator

The numerator $24468−15206 = 9262$, and the denominator $2015 - 2000=15$.

Step4: Calculate the average rate of change

$\frac{9262}{15}\approx617.47$.

Answer:

The average rate of change between 2000 and 2015 is approximately 617.47 producing gas - wells per year.