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

Answer:

$f(x)=\frac{1}{2}(5)^x$ eventually exceeds $g(x)=6x + 2$.

Explanation:

Step1: Identify function types

$f(x)$ is an exponential function with base $5>1$, $g(x)$ is a linear function.

Step2: Recall growth - rate property

Exponential functions $y = a\cdot b^x$ ($a>0,b > 1$) grow faster than linear functions $y=mx + c$ as $x\to+\infty$.

Step3: Conclusion

As $x$ gets larger and larger, the exponential function $f(x)=\frac{1}{2}(5)^x$ will eventually exceed the linear function $g(x)=6x + 2$.