To determine when there are 81 players in the online game, we need to solve the equation [tex]\( f(x) = 81 \)[/tex] where [tex]\( f(x) = 3^x \)[/tex].
Step-by-Step Solution:
1. Start with the equation representing the number of players:
[tex]\[
3^x = 81
\][/tex]
2. Recognize that 81 can be expressed as a power of 3:
[tex]\[
81 = 3^4
\][/tex]
3. Substitute [tex]\( 81 \)[/tex] with [tex]\( 3^4 \)[/tex] in the equation:
[tex]\[
3^x = 3^4
\][/tex]
4. Since the bases are equal, the exponents must also be equal:
[tex]\[
x = 4
\][/tex]
Therefore, [tex]\( x = 4 \)[/tex]. This means there are 81 players in week 4.
The correct answer is:
D. Week 4
