Question

given the functions $f(x) = 5x^3$ and $g(x) = 2^x$, which of the following statements is true?
answer
$\circ$ $f(11)=g(11)$ $\circ$ $f(11)>g(11)$ $\circ$ $f(11)

Explanation:

Step1: Calculate f(11)

Substitute \( x = 11 \) into \( f(x)=5x^{3} \). So \( f(11)=5\times(11)^{3} \). First, calculate \( 11^{3}=11\times11\times11 = 1331 \). Then, \( 5\times1331 = 6655 \).

Step2: Calculate g(11)

Substitute \( x = 11 \) into \( g(x)=2^{x} \). So \( g(11)=2^{11} \). We know that \( 2^{10}=1024 \), so \( 2^{11}=2^{10}\times2 = 1024\times2 = 2048 \).

Step3: Compare f(11) and g(11)

We have \( f(11)=6655 \) and \( g(11)=2048 \). Since \( 6655>2048 \), we get \( f(11)>g(11) \).

Answer:

\( f(11) > g(11) \)