Question

The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 1 and x = 3.

Answer 1

The average rate of change can be found by striking a line between the two endpoints and finding the slope thereof:

$ROC_{ave}=m_{1-2}$
$m_{1-2} = \frac{f(x_2)-f(x_1)}{x_2-x_1} = \frac{f(3)-f(1)}{3-1}$

Solve for f(3) & f(1), substitute into the slope formula and compute. 

$m_{1-2} = \frac{9-3}{3-1}$ 

$m_{1-2} = \frac{6}{2} = 3$