Question

the following chart shows student population in a certain elementary school over a 5 year period.

what is the average rate of change in the number of students from 2010 to 2012? students/year

what is the average rate of change in the number of students from 2011 to 2014? students/year

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Explanation:

Step1: Calculate average rate of change from 2010 to 2012

The formula for average rate of change is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 2010$, $y_1=655$, $x_2 = 2012$, $y_2 = 735$.
$\frac{735 - 655}{2012 - 2010}=\frac{80}{2}$

Step2: Calculate average rate of change from 2011 to 2014

Using the same formula, $x_1 = 2011$, $y_1 = 700$, $x_2=2014$, $y_2 = 770$.
$\frac{770 - 700}{2014 - 2011}=\frac{70}{3}\approx23.33$

Answer:

1. $40$ Students/Year
2. $\approx23.33$ Students/Year