Question

question
given the functions $f(x) = 3x^8$ and $g(x) = 10cdot 6^x$, which of the following statements is true?
answer
$\circ$ $f(3) < g(3)$ $\circ$ $f(3) > g(3)$ $\circ$ $f(3) = g(3)$

Explanation:

Step1: Calculate \( f(3) \)

Substitute \( x = 3 \) into \( f(x)=3x^{8} \).
\( f(3)=3\times3^{8}=3^{1 + 8}=3^{9} \). Calculate \( 3^{9}=19683 \).

Step2: Calculate \( g(3) \)

Substitute \( x = 3 \) into \( g(x)=10\cdot6^{x} \).
\( g(3)=10\times6^{3}=10\times216 = 2160 \).

Step3: Compare \( f(3) \) and \( g(3) \)

Since \( 19683>2160 \), we have \( f(3)>g(3) \).

Answer:

\( f(3) > g(3) \)