Question

Find the rate of change

Answer 1

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ h(x)= 2^x \qquad \stackrel{2\le x\le 4}{\begin{cases} x_1=2\\ x_2=4 \end{cases}}\implies \cfrac{h(4)-h(2)}{4-2}\implies \cfrac{2^4-2^2}{2} \\\\\\ \cfrac{16-4}{2}\implies \cfrac{12}{2}\implies 6$