Question

For f(x) = 0.01(2)x, find the average rate of change from x = 2 to x = 10.

Answer 1

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ f(x)=0.01(2)^x \qquad \begin{cases} x_1=2\\ x_2=10 \end{cases}\implies \cfrac{f(10)-f(2)}{10-2} \\\\\\ \cfrac{0.01(2)^{10}~~-~~0.01(2)^2}{8}\implies \cfrac{10.24~~-~~0.04}{8}\\\\\\ \cfrac{10.20}{8}\implies 1.275$

Answer 2

Your correct answer will be 1.275