# If a company earned $100,000 in 1980 and$400,000 in 2010, what was its average rate of change per year?

Sep 28, 2014

The average rate of change is the slope of the secant line or just line that intersects $2$ points on a graph.

If you think of the information as coordinates on a graph the points would be $\left(1980 , 10000\right)$ and $\left(2010 , 400000\right) .$

$\left({x}_{1} , {y}_{1}\right) \to \left(1980 , 10000\right)$
$\left({x}_{2} , {y}_{2}\right) \to \left(2010 , 40000\right)$

Average rate of change =

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{400000 - 100000}{2010 - 1980} = \frac{300000}{30} = \frac{30000}{3} = 10000$

The average rate of change per year is \$10000.