given the functions: $f(x)=5x + 12$ and $g(x)=2^{x}-20$.\ngraph the functions to determine which value of…

given the functions: $f(x)=5x + 12$ and $g(x)=2^{x}-20$.\ngraph the functions to determine which value of $x$ is closest to where $g(x)$ begins to exceed $f(x)$.\na $x = 5$\nb $x = 6$\nc $x = 7$\nd $x = 8$

given the functions: $f(x)=5x + 12$ and $g(x)=2^{x}-20$.\ngraph the functions to determine which value of $x$ is closest to where $g(x)$ begins to exceed $f(x)$.\na $x = 5$\nb $x = 6$\nc $x = 7$\nd $x = 8$

Answer

Answer:

A. (x = 5)

Explanation:

Step1: Calculate (f(x)) and (g(x)) for (x = 5)

For (f(x)=5x + 12), substitute (x = 5): (f(5)=5\times5+12=25 + 12=37) For (g(x)=2^{x}-20), substitute (x = 5): (g(5)=2^{5}-20=32-20 = 12) ((g(x)<f(x)))

Step2: Calculate (f(x)) and (g(x)) for (x = 6)

For (f(x)=5x + 12), substitute (x = 6): (f(6)=5\times6+12=30 + 12=42) For (g(x)=2^{x}-20), substitute (x = 6): (g(6)=2^{6}-20=64-20 = 44) ((g(x)>f(x)))

Since at (x = 5), (g(x)<f(x)) and at (x = 6), (g(x)>f(x)), the value of (x) closest to where (g(x)) begins to exceed (f(x)) is (x = 5).