Question

aa.11 compare linear and exp both of these functions grow as x gets larger and larger. which function eventually exceeds the other? f(x) = 10x + 9 g(x) = 3(4)^x - 5 submit

Explanation:

Step1: Analyze function types

$f(x) = 10x + 9$ is a linear function (degree 1), and $g(x) = 3(4)^x - 5$ is an exponential function (base $4>1$).

Step2: Recall growth rates

Exponential functions with base $>1$ grow faster than linear functions as $x$ becomes large. This is because the exponent in the exponential function causes it to increase multiplicatively, while the linear function increases additively.

Step3: Compare growth for large $x$

For large values of $x$, the term $3(4)^x$ in $g(x)$ will dominate and grow much faster than the $10x$ term in $f(x)$. So $g(x)$ will eventually exceed $f(x)$.

Answer:

$g(x) = 3(4)^x - 5$