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

Explanation:

Step1: Identify function types

$f(x)=1.2(3)^{x-1}$ is exponential; $g(x)=5.6x+2$ is linear.

Step2: Compare growth rates

Exponential functions with base $>1$ grow faster than linear functions as $x\to\infty$.

Step3: Verify with large $x$

For $x=5$: $f(5)=1.2(3)^{4}=1.2\times81=97.2$; $g(5)=5.6\times5+2=30$. For $x=10$: $f(10)=1.2(3)^{9}=1.2\times19683=23619.6$; $g(10)=5.6\times10+2=58$.

Answer:

The exponential function $f(x) = 1.2(3)^{x-1}$ eventually exceeds the linear function $g(x) = 5.6x + 2$ as $x$ becomes larger.