Final answer:
The explicit function is y = 4^(x-1); it is an exponential function representing the geometric sequence where each term is 4 times the previous term. The given options do not include the correct answer.
Step-by-step explanation:
To find the explicit function for the sequence 1/4, 1, 4, 16, 64, ... we look for a pattern in the sequence. Notice how each term is 4 times the previous term: 1/4 × 4 = 1, 1 × 4 = 4, 4 × 4 = 16, and so on. This is a geometric sequence with a common ratio of 4. The first term (when x=1) is 1/4. Therefore, we can write the nth term as an = (1/4) × 4n-1.
To express this sequence as a function of x, where x corresponds to the position of the term in the sequence starting with x=1 for the first term, the explicit function can be represented as: y = (1/4) × 4x-1, which simplifies to y = 4x-1.
Comparing this function to the answer choices:
A) y = 4 (x - 1) is linear and does not represent the exponential growth of our sequence.
B) y = 4x is close but does not give us 1/4 when x=1.
C) y = 1 / 4x represents an exponential decay, not growth.
D) y = x2 describes a quadratic relationship, not exponential.
Therefore, none of the given options correctly represent the sequence, so there might be an error in the options provided.