Final Answer:
A. Proportional because The relationship is proportional because the change in 'r' is consistently determined by the square of 'b,' indicating a constant ratio.
Step-by-step explanation:
The given relationship, r = b^2 + 1, is a proportional situation. In a proportional relationship, two variables are related by a constant ratio. In this case, the relationship between r and b is determined by the square of b plus 1. When b is multiplied by a constant, the resulting value of r will be directly proportional to b.
The presence of the square term indicates a nonlinear relationship, but it is still proportional because the change in b leads to a consistent and predictable change in r. Therefore, despite the nonlinearity introduced by the square term, the relationship is fundamentally proportional.
The constant ratio between r and the square of b establishes the proportional nature of this mathematical relationship.