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

Answer:

The function $g(x)=4^{x}-5$ eventually exceeds the function $f(x)=4x + 5$.

Explanation:

Step1: Analyze function types

$f(x)$ is a linear function, $g(x)$ is an exponential function.

Step2: Recall growth - rate properties

Exponential functions ($y = a^{x}$, $a>1$) grow faster than linear functions ($y=mx + b$) as $x\rightarrow+\infty$. Here $a = 4>1$, $m = 4$, $b = 5$.

Step3: Conclusion

As $x$ gets larger and larger, $g(x)=4^{x}-5$ will eventually be greater than $f(x)=4x + 5$.