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The number of players of an online game triples each week. The function [tex]f(x)=3^x[/tex] represents the number of players in week [tex]x[/tex]. When are there 81 players?

A. Week 9
B. Week 3
C. Week 27
D. Week 4

Sagot :

GinnyAnswer
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
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