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The number of people contacted at each level of a phone tree can be represented by [tex]f(x)=3^x[/tex], where [tex]x[/tex] represents the level.

What is [tex]x[/tex] when [tex]f(x)=27[/tex]?

A. [tex]x=2[/tex]; At level 2, 27 people will be contacted.
B. [tex]x=24[/tex]; At level 24, 27 people will be contacted.
C. [tex]x=3[/tex]; At level 3, 27 people will be contacted.
D. [tex]x=9[/tex]; At level 9, 27 people will be contacted.

Sagot :

GinnyAnswer
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.
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