Given the input-output pairs (2, 4), (3, 16), (4, 64), (5, 256), which of the following rules best describes the relationship? A. y = 4x − 1 B. y = 2x − 1 C. y = 4^(x-1) D. y = 4^x

We are given a set of input values (x) and their corresponding output values (y).
For x = 2, y = 4
For x = 3, y = 16
For x = 4, y = 64
For x = 5, y = 256

Notice that the output values are powers of 4:
$4 = 4^1$
$16 = 4^2$
$64 = 4^3$
$256 = 4^4$

We need a rule $y = 4^{\text{exponent}}$ where the exponent depends on x.
If the exponent is $x-1$:
For x = 2, exponent is $2-1 = 1$, so $y = 4^1 = 4$.
For x = 3, exponent is $3-1 = 2$, so $y = 4^2 = 16$.
For x = 4, exponent is $4-1 = 3$, so $y = 4^3 = 64$.
For x = 5, exponent is $5-1 = 4$, so $y = 4^4 = 256$.
This pattern matches all the given values.

The rule that fits the mapping is $y = 4^{x-1}$.
Comparing this with the given options:
A. $y = 4x - 1$
B. $y = 2x - 1$
C. $y = 4^{x-1}$
D. $y = 4^x$

The correct option is C.

The final answer is $\boxed{\text{C. } y = 4^{x-1}}$.