In the given equation, C(p) = 5p² + 70, p represents the total number of additional pairs of shoes purchased, and C represents the total cost in dollars. Since the number of additional pairs of shoes cannot be negative (as it represents additional pairs), we can eliminate option B (-33) because it is a negative value.
To determine the values that make sense in the context of the problem, we need to consider the domain of the function. In this case, the domain represents the valid values for p that we can input into the equation to calculate the cost.
Let's analyze the remaining options:
A. 1/2: This value represents half a pair of shoes, which is not a practical or meaningful quantity. It doesn't make sense in the context of the problem, so option A can be eliminated.
C. 7.5: This value represents 7.5 additional pairs of shoes, which is a meaningful quantity. It makes sense in the context of the problem as you can purchase additional pairs of shoes in fractions (such as half a pair or a quarter pair).
D. 20: This value represents 20 additional pairs of shoes, which is a reasonable quantity to consider when purchasing multiple pairs of athletic shoes.
Based on the analysis, the values that make sense in the context of this problem are:
C. 7.5
D. 20
Therefore, the correct options are C and D.