Question

what is the slope of the secant line that intersects the graph of $g(x)=3^{2x}$ at $x = 0$ and $x = 2$?

Explanation:

Step1: Find function values at given points

First, find $g(0)$ and $g(2)$.
For $x = 0$, $g(0)=3^{2\times0}=3^0 = 1$.
For $x = 2$, $g(2)=3^{2\times2}=3^4 = 81$.

Step2: Use slope formula

The slope $m$ of a secant - line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = g(0)=1,x_2 = 2,y_2 = g(2)=81$.
So, $m=\frac{g(2)-g(0)}{2 - 0}=\frac{81 - 1}{2}=\frac{80}{2}=40$.

Answer:

40