Question

For the graphed function f(x) = (4)x − 1 + 2, calculate the average rate of change from x = 1 to x = 2.

Answer 1

Average rate of the function: 3

Step-by-step explanation:

The function in this problem is

$f(x)=4^{x-1}+2$

The average rate of change of a function over an interval $(x_1,x_2)$ is given by

$r=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

where

$f(x_1),f(x_2)$ are the values of the function calculated in $x_1,x_2$ respectively

For the function in this problem we have:

$x_1=1$, so

$f(x_1)=f(1)=4^{1-1}+2=4^0+2=1+2=3$

$x_2=2$, so

$f(x_2)=f(2)=4^{2-1}+2=4^1+2=4+2=6$

So, the average rate of change is

$r=\frac{6-3}{2-1}=\frac{3}{1}=3$

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