Let's calculate $f(9)$ and $g(9)$ using the given functions to determine the correct answer.

Given Functions:

1. $f(x) = 5x^4$
2. $g(x) = 6 \cdot 3^x$

Step 1: Calculate $f(9)$

$f(9) = 5 \cdot 9^4$ $9^4 = 6561$ $f(9) = 5 \cdot 6561 = 32805$

Step 2: Calculate $g(9)$

$g(9) = 6 \cdot 3^9$ $3^9 = 19683$ $g(9) = 6 \cdot 19683 = 118098$

Step 3: Compare $f(9)$ and $g(9)$

• $f(9) = 32805$
• $g(9) = 118098$

Since $32805 < 118098$, the correct statement is:

$f(9) < g(9)$

Final Answer:

$f(9) < g(9)$ is the correct statement.

Would you like more details or have any questions? Here are five related questions:

1. How do you determine the growth rate of different types of functions?
2. What is the significance of the base in exponential functions?
3. How would the comparison change if $x$ were smaller?
4. Can you find other values of $x$ where $f(x)$ and $g(x)$ might be equal?
5. What does the calculation tell you about the nature of polynomial vs. exponential functions?

Tip: When comparing functions, it helps to evaluate them at specific points to understand their relative sizes.