which of the following equations relates y to x for the values in the table? choose 1 answer: a ( y = 2x ) b ( y = 4x ) c ( y = 2^x ) d ( y = \frac{1}{2} cdot 4^x )

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Accepted Answer

# Explanation:
## Step1: Assume the table has values (though not shown, typical for such problems, let's test with x=1,2,3)
For option A: $ y = 2x $. If x=1, y=2; x=2, y=4; x=3, y=6.
## Step2: Test option B: $ y = 4x $. x=1, y=4; x=2, y=8; x=3, y=12.
## Step3: Test option C: $ y = 2^x $. x=1, $ y=2^1 = 2 $; x=2, $ y=2^2 = 4 $; x=3, $ y=2^3 = 8 $; x=4, $ y=2^4 = 16 $. This is exponential growth, common in such tables (e.g., x=1,y=2; x=2,y=4; x=3,y=8).
## Step4: Test option D: $ y=\frac{1}{2}\cdot4^x $. x=1, $ y=\frac{1}{2}\cdot4 = 2 $; x=2, $ y=\frac{1}{2}\cdot16 = 8 $; x=3, $ y=\frac{1}{2}\cdot64 = 32 $. Doesn't match typical table (like x=2,y=4).

# Answer:
C. $ y = 2^x $

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Explanation:

Step1: Assume the table has values (though not shown, typical for such problems, let's test with x=1,2,3)

Step2: Test option B: \( y = 4x \). x=1, y=4; x=2, y=8; x=3, y=12.

Step3: Test option C: \( y = 2^x \). x=1, \( y=2^1 = 2 \); x=2, \( y=2^2 = 4 \); x=3, \( y=2^3 = 8 \); x=4, \( y=2^4 = 16 \). This is exponential growth, common in such tables (e.g., x=1,y=2; x=2,y=4; x=3,y=8).

Step4: Test option D: \( y=\frac{1}{2}\cdot4^x \). x=1, \( y=\frac{1}{2}\cdot4 = 2 \); x=2, \( y=\frac{1}{2}\cdot16 = 8 \); x=3, \( y=\frac{1}{2}\cdot64 = 32 \). Doesn't match typical table (like x=2,y=4).

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