both of these functions grow as x gets larger and larger. which function eventually exceeds the…

Answer:

$g(x) = 3^{x}$ eventually exceeds $f(x)=5x^{2}-8$.

Explanation:

Step1: Recall growth - rate of functions

Exponential functions $a^{x}$ ($a>1$) grow faster than polynomial functions $b_nx^n + b_{n - 1}x^{n - 1}+\cdots + b_0$ as $x\to+\infty$. Here, $f(x)=5x^{2}-8$ is a polynomial function of degree $n = 2$ and $g(x)=3^{x}$ is an exponential function with $a = 3>1$. As $x$ gets larger and larger, the exponential function $g(x)=3^{x}$ will eventually be larger than the polynomial function $f(x)=5x^{2}-8$.