Question

question 25 of 25
the number of players of an online game triples each week. the function
$f(x) = 3^x$ represents the number of players in week $x$. when are there 81
players?

\\(\bigcirc\\) a. week 9

\\(\bigcirc\\) b. week 27

\\(\bigcirc\\) c. week 3

\\(\bigcirc\\) d. week 4

Explanation:

Step1: Set up the equation

We know the function is \( f(x) = 3^x \) and we want to find \( x \) when \( f(x)=81 \). So we set up the equation \( 3^x = 81 \).

Step2: Solve for x

We know that \( 81 = 3^4 \) (since \( 3\times3\times3\times3 = 81 \)). So the equation becomes \( 3^x = 3^4 \). Since the bases are the same, we can set the exponents equal to each other, so \( x = 4 \).

Answer:

D. Week 4