To find the equation that represents the sequence \(4, 16, 64, 256, 1024, \ldots\), let's first observe the pattern in the terms.
- The first term is \(4\), which can be written as \(4^1\).
- The second term is \(16\), which can be written as \(4^2\).
- The third term is \(64\), which can be written as \(4^3\).
- The fourth term is \(256\), which can be written as \(4^4\).
- The fifth term is \(1024\), which can be written as \(4^5\).
From this observation, we can see that the \(n\)th term of the sequence can be represented by the equation:
\[ y = 4^n \]
Since the terms are indexed starting from the first term as \(n=1\), we can adjust the representation to fit our options.
Given the provided choices, the equation that fits this pattern is:
y = 4^x
Therefore, the correct choice is:
y = 4^x (which is equivalent to y = 4^n if we start counting from \(n = 1\)).