Question

Given the functions f, of, x, equals, 4, x, to the power 5f(x)=4x
5
and g, of, x, equals, 7, dot, 3, to the power xg(x)=7⋅3
x
, which of the following statements is true?
Answer
Multiple Choice Answers
f, of, 7, is greater than, g, of, 7f(7)>g(7)
f, of, 7, equals, g, of, 7f(7)=g(7)
f, of, 7, is less than, g, of, 7f(7)<g(7)

Answer 1

To determine which of the statements is true, we need to calculate \( f(7) \) and \( g(7) \).

Given:
- \( f(x) = 4x^5 \)
- \( g(x) = 7 \cdot 3^x \)

Now, let's calculate each function at \( x = 7 \).

**Calculating \( f(7) \):**
\[
f(7) = 4 \cdot 7^5
\]
Calculating \( 7^5 \):
\[
7^5 = 16807
\]
So,
\[
f(7) = 4 \cdot 16807 = 67228
\]

**Calculating \( g(7) \):**
\[
g(7) = 7 \cdot 3^7
\]
Calculating \( 3^7 \):
\[
3^7 = 2187
\]
So,
\[
g(7) = 7 \cdot 2187 = 15309
\]

Now we compare \( f(7) \) and \( g(7) \):
- \( f(7) = 67228 \)
- \( g(7) = 15309 \)

Since \( 67228 > 15309 \), we have:
\[
f(7) > g(7)
\]

Thus, the correct statement is:
\[
\boxed{f(7) > g(7)}
\]