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

Answer:

$g(x)=\frac{3}{4}(5)^{x}$ eventually exceeds $f(x)=\frac{15}{4}x + 3$.

Explanation:

Step1: Identify function types

$f(x)$ is linear, $g(x)$ is exponential.

Step2: Recall growth - rate property

Exponential functions ($a\cdot b^{x}$, $b>1$) grow faster than linear functions ($mx + c$) as $x\to+\infty$.

Step3: Analyze given functions

For $f(x)=\frac{15}{4}x + 3$ (linear) and $g(x)=\frac{3}{4}(5)^{x}$ (exponential with $b = 5>1$), as $x$ gets very large, $g(x)$ will be larger than $f(x)$.