Question

10 POINTS. NEED THIS ASAP!!

What is the average rate of change of the function on the interval from x = 0 to x = 5?
f(x)=1/2(3)^x

Enter your answer, as a decimal, in the box.

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}\\\\ -------------------------------`


`\bf f(x)= \cfrac{1}{2}(3)^x \qquad \begin{cases} x_1=0\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(0)}{5-0} \\\\\\ \cfrac{(1)/(2)(3)^5~~-~~(1)/(2)(3)^0}{5}\implies \cfrac{(3^5)/(2)~~-~~(1)/(2)}{5}\implies \cfrac{(243)/(2)-(1)/(2)}{5} \\\\\\ \cfrac{(243-1)/(2)}{(5)/(1)}\implies \cfrac{(242)/(2)}{(5)/(1)}\implies \cfrac{242}{2}\cdot \cfrac{1}{5}\implies \cfrac{242}{10}\implies \cfrac{121}{5}`