MATH SOLVE

4 months ago

Q:
# 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)^xEnter your answer, as a decimal, in the box.

Accepted Solution

A:

[tex]\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}\\\\
-------------------------------[/tex]

[tex]\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{\frac{1}{2}(3)^5~~-~~\frac{1}{2}(3)^0}{5}\implies \cfrac{\frac{3^5}{2}~~-~~\frac{1}{2}}{5}\implies \cfrac{\frac{243}{2}-\frac{1}{2}}{5} \\\\\\ \cfrac{\frac{243-1}{2}}{\frac{5}{1}}\implies \cfrac{\frac{242}{2}}{\frac{5}{1}}\implies \cfrac{242}{2}\cdot \cfrac{1}{5}\implies \cfrac{242}{10}\implies \cfrac{121}{5}[/tex]

[tex]\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{\frac{1}{2}(3)^5~~-~~\frac{1}{2}(3)^0}{5}\implies \cfrac{\frac{3^5}{2}~~-~~\frac{1}{2}}{5}\implies \cfrac{\frac{243}{2}-\frac{1}{2}}{5} \\\\\\ \cfrac{\frac{243-1}{2}}{\frac{5}{1}}\implies \cfrac{\frac{242}{2}}{\frac{5}{1}}\implies \cfrac{242}{2}\cdot \cfrac{1}{5}\implies \cfrac{242}{10}\implies \cfrac{121}{5}[/tex]