Question

given the functions $f(x) = 4x^5$ and $g(x) = 7\cdot 3^x$, which of the following statements is true?
answer
$\circ$ $f(7) > g(7)$ $\circ$ $f(7) = g(7)$ $\circ$ $f(7) < g(7)$

Explanation:

Step1: Calculate \( f(7) \)

To find \( f(7) \), substitute \( x = 7 \) into \( f(x)=4x^{8} \).
\( f(7)=4\times7^{8} \)
First, calculate \( 7^{8}=7\times7\times7\times7\times7\times7\times7\times7 = 5764801 \)
Then, \( f(7)=4\times5764801 = 23059204 \)

Step2: Calculate \( g(7) \)

To find \( g(7) \), substitute \( x = 7 \) into \( g(x)=7\cdot3^{x} \).
\( g(7)=7\times3^{7} \)
First, calculate \( 3^{7}=3\times3\times3\times3\times3\times3\times3 = 2187 \)
Then, \( g(7)=7\times2187 = 15309 \)

Step3: Compare \( f(7) \) and \( g(7) \)

We have \( f(7)=23059204 \) and \( g(7)=15309 \).
Since \( 23059204>15309 \), we get \( f(7)>g(7) \).

Answer:

\( f(7) > g(7) \) (the option " \( f(7) > g(7) \)")