Question

For the graphed exponential equation, calculate the average rate of change of change from x=4 to x=8

Answer 1

If you look at the picture, when

x = 4, y = 20,

and when

x = 8, y = 10

thus

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ \begin{cases} x_1=4\\ x_2=8 \end{cases}\implies \cfrac{f(8)-f(4)}{8-4}\implies \cfrac{10-20}{4}\implies \cfrac{-10}{4}\implies -\cfrac{5}{2}$