use the graphing calculator to graph these functions: y1 = 2x ; y2 = 2x^2 ; y3 = 2^x. after what y - value…
use the graphing calculator to graph these functions: y1 = 2x ; y2 = 2x^2 ; y3 = 2^x. after what y - value does the exponential function appear to surpass the linear function?
Answer
Explanation:
Step1: Set the linear function $y_1 = 2x$ and the exponential function $y_3=2^x$.
We want to find when $2^x>2x$.
Step2: Test some values of $x$.
When $x = 1$, $y_1=2\times1 = 2$ and $y_3=2^1 = 2$, so $y_1=y_3$. When $x = 2$, $y_1=2\times2 = 4$ and $y_3=2^2 = 4$, so $y_1=y_3$. When $x = 3$, $y_1=2\times3=6$ and $y_3=2^3 = 8$, so $y_3>y_1$. At $x = 3$, $y_1 = 6$.
Answer:
6