use the graphing calculator to graph these functions: y1 = 2x; y2 = 2x^2; y3 = 2^x. after what y - value…

Explanation:

Step1: Set up the functions

We have $y_1 = 2x$, $y_3=2^x$.

Step2: Find the intersection point

Set $2x = 2^x$. By trial - and - error: When $x = 1$, $y_1=2\times1 = 2$ and $y_3 = 2^1=2$. When $x = 2$, $y_1=2\times2 = 4$ and $y_3 = 2^2 = 4$. When $x = 3$, $y_1=2\times3=6$ and $y_3 = 2^3 = 8$.

Step3: Determine the $y$-value

Since at $x = 2$, $y_1=y_3 = 4$ and at $x = 3$, $y_3>y_1$, the $y$-value after which the exponential function surpasses the linear function is $y = 4$.

Answer:

4