Final answer:
The correct answer is option D) 7, but the question contains a misconception. The equation Y=3x⁴+7 does not have a first common difference because it is not linear. The '7' in the equation is the constant term, not a difference.
Step-by-step explanation:
The correct answer is option D) 7.
When discussing equations, a linear equation is one that has the highest exponent of the variable being 1, resulting in a straight line when graphed. The equation Y=3x⁴+7 is not a linear equation because the highest exponent of x is 4. However, if we consider the sequence of values of Y for consecutive integer values of x, the sequence itself does not have a constant difference because it is determined by a polynomial of degree 4. The question appears to be a misunderstanding as it mixes the concept of a linear equation with the concept of a polynomial equation.
Nonetheless, interpreting the question literally, the value of 7 in the equation does not represent the first common difference, as the first common difference is applicable to linear equations and sequences, not polynomials. The '7' in the equation is actually the constant term of the polynomial, and in the context of sequences, there is no 'first common difference' for a polynomial of degree 4.
Therefore, if we had to match the equation with a numbered first common difference, we could say that there is no applicable option. The polynomial equation given does not allow for a meaningful first common difference to be extracted.