Question

given the functions $f(x) = 4x^4$ and $g(x) = 4 \cdot 3^x$, which of the following statements is true?
answer
$\circ$ $f(5) = g(5)$ $\circ$ $f(5) < g(5)$
$\circ$ $f(5) > g(5)$

Explanation:

Step1: Calculate \( f(5) \)

Substitute \( x = 5 \) into \( f(x)=4x^{4} \).
\( f(5)=4\times5^{4}=4\times625 = 2500 \)

Step2: Calculate \( g(5) \)

Substitute \( x = 5 \) into \( g(x)=4\cdot3^{x} \).
\( g(5)=4\times3^{5}=4\times243 = 972 \)

Step3: Compare \( f(5) \) and \( g(5) \)

Since \( 2500>972 \), we have \( f(5)>g(5) \).

Answer:

\( f(5) > g(5) \) (the option with \( f(5) > g(5) \))