Find the average rate of change over the given interval: f(x) = 3^x, [1, 4]

Mathematics

1 answer:

GREYUIT [131]2 years ago

3 0

$\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\
f(x)= 3^x \qquad 
\stackrel{[1,4]}{\begin{cases}
x_1=1\\
x_2=4
\end{cases}}\implies \cfrac{f(4)-f(1)}{4-1}\implies \cfrac{3^4~-~3^1}{3}
\\\\\\
\cfrac{81-3}{3}\implies \cfrac{78}{3}\implies 26$

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