To find an accurate formula for the given sequence \(2, 3.5, 6.125, 10.71875\), we can analyze the sequence for its pattern.
- The first term is \(2\).
- The second term \(3.5\) can be viewed as \(2 \times 1.75\).
- The third term \(6.125\) can be viewed as \(3.5 \times \frac{6.125}{3.5} \approx 1.75\).
- The fourth term \(10.71875\) can be obtained from \(6.125 \times \frac{10.71875}{6.125} \approx 1.75\).
The ratio increases multiplicatively by a factor close to \(1.75\) for each term.
Considering the available responses:
- Option: \(y = 2 + 1.75x\) suggests a linear relationship, which is not applicable here since the growth appears to be exponential.
- Option: \(y = 2(1.75)^{x-1}\) reflects an exponential growth starting at \(2\), which correctly represents the sequence.
- Option: \(y = 2(1.5)^x\) does not fit the growth factor for this particular sequence.
- Option: \(y = 21.5^x\) suggests a much larger growth factor and does not relate to the initial values.
The most accurate formula for the sequence would be:
y = 2(1.75)^{x-1}
Thus, the correct response is: y = 2(1.75)^{x-1}.