use the graphing calculator to graph these functions: $y_1 = 2x;y_2 = 2x^{2};y_3 = 2^{x}$ after what y…

use the graphing calculator to graph these functions: $y_1 = 2x;y_2 = 2x^{2};y_3 = 2^{x}$ after what y - value does the exponential function appear to surpass the linear function? 4 complete after approximately what y - value does the exponential function surpass the quadratic function? retry

use the graphing calculator to graph these functions: $y_1 = 2x;y_2 = 2x^{2};y_3 = 2^{x}$ after what y - value does the exponential function appear to surpass the linear function? 4 complete after approximately what y - value does the exponential function surpass the quadratic function? retry

Answer

Explanation:

Step1: Set the exponential function equal to the quadratic function

Set $y_2 = y_3$, so $2x^{2}=2^{x}$.

Step2: Solve by trial - and - error or graphing

We can try some integer values of $x$. When $x = 4$, $y_2=2\times4^{2}=2\times16 = 32$ and $y_3=2^{4}=16$. When $x = 5$, $y_2=2\times5^{2}=2\times25 = 50$ and $y_3=2^{5}=32$. When $x= 6$, $y_2=2\times6^{2}=2\times36 = 72$ and $y_3=2^{6}=64$. When $x = 8$, $y_2=2\times8^{2}=2\times64 = 128$ and $y_3=2^{8}=256$. By graphing $y = 2x^{2}$ and $y = 2^{x}$ (using a graphing calculator as suggested), we can see that the exponential function $y = 2^{x}$ surpasses the quadratic function $y = 2x^{2}$ around $y = 128$.

Answer:

128