what is the average rate of change of y = 2(3)^x at 2, 4? 630 3 36.8 72

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 4$, and $y=f(x)=2(3)^{x}$.

Step2: Calculate $f(2)$

Substitute $x = 2$ into $y = 2(3)^{x}$: $f(2)=2\times3^{2}=2\times9 = 18$.

Step3: Calculate $f(4)$

Substitute $x = 4$ into $y = 2(3)^{x}$: $f(4)=2\times3^{4}=2\times81 = 162$.

Step4: Calculate average rate of change

$\frac{f(4)-f(2)}{4 - 2}=\frac{162-18}{2}=\frac{144}{2}=72$.