Question

For f(x)=0.01(2)power of x, find the average rate of change from x=3 to x=8

Answer 1

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ f(x)= 0.01(2)^x \qquad \begin{cases} x_1=3\\ x_2=8 \end{cases}\implies \cfrac{f(8)-f(3)}{8-3} \\\\\\ \cfrac{0.01(2)^8-0.01(2)^3}{8-3}$