What is the average rate of change of the function $f(x)=2(3)^x$ from x=2 to x=4?

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Answer 1 · 2017-02-24T04:41:50

Use the slope formula to find the average rate of change:
$m=frac{y_2-y_1}{x_2-x_1}$

$m=frac{f(4)-f(2)}{4-2}$

To simplify this, we need to find values of $f(4)$ and $f(2)$ :
$f(4)=2(3)^4 = 2(81)=162$
$f(2)=2(3)^2=2(9)=18$

$m=frac{162-18}{2}$

$m=144/2$

$m=72$

What is the average rate of change of the function f(x)=2(3)^xf(x)=2(3)^x from x=2 to x=4?