Question

Can someone read the question and give me answer with explanation, please.

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)=20\left( (1)/(4) \right)^x \qquad \begin{cases} x_1=1\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(1)}{2-1} \\\\\\ \cfrac{20\left( (1)/(4) \right)^2~~-~~20\left( (1)/(4) \right)^1}{1}\implies \cfrac{20\cdot (1^2)/(4^2)~~-~~20\cdot (1^1)/(4^1)}{1} \\\\\\ \cfrac{(20)/(16)-(20)/(4)}{1}\implies \cfrac{(5)/(4)-5}{1}\implies \cfrac{(5-20)/(4)}{1}\implies \cfrac{-(15)/(4)}{1}\implies -\cfrac{15}{4}\implies -3(3)/(4)`