Question

1. which of the following equations is best represented by the table below?

x	0	1	2	3	4
y	1	4	16	64	256

options:

• ( y = 4^x )
• ( y = 2^x )
• ( y = 2^x + 1 )
• ( y = 4^x + 1 )

Explanation:

Step1: Test $x=0$ on all equations

For $y=4^x$: $y=4^0=1$
For $y=2^x$: $y=2^0=1$
For $y=2^x+1$: $y=2^0+1=2$
For $y=4^x+1$: $y=4^0+1=2$

Step2: Eliminate mismatched equations

The table has $y=1$ when $x=0$, so eliminate $y=2^x+1$ and $y=4^x+1$.

Step3: Test $x=1$ on remaining equations

For $y=4^x$: $y=4^1=4$
For $y=2^x$: $y=2^1=2$

Step4: Eliminate mismatched equation

The table has $y=4$ when $x=1$, so eliminate $y=2^x$.

Step5: Verify with $x=2,3,4$

For $x=2$: $y=4^2=16$ (matches table)
For $x=3$: $y=4^3=64$ (matches table)
For $x=4$: $y=4^4=256$ (matches table)

Answer:

A. $y=4^x$