To find the level [tex]\( x \)[/tex] in the phone tree where 27 people are contacted, we need to solve the equation [tex]\( f(x) = 3^x \)[/tex] for [tex]\( x \)[/tex], given that [tex]\( f(x) = 27 \)[/tex].
So, we start with the equation:
[tex]\[ 3^x = 27 \][/tex]
We need to determine what power [tex]\( x \)[/tex] of 3 gives us 27. We use our knowledge of exponents to see if 27 can be expressed as a power of 3.
We know that:
[tex]\[ 3^1 = 3 \][/tex]
[tex]\[ 3^2 = 9 \][/tex]
[tex]\[ 3^3 = 27 \][/tex]
Therefore, we can see that:
[tex]\[ 3^3 = 27 \][/tex]
So, [tex]\( x \)[/tex] must be 3.
Therefore, the correct answer is:
C. [tex]\( x=3 \)[/tex]; At level 3, 27 people will be contacted.
