Suppose that in a particular state a standardized test is given to all graduating seniors. Let score denote a student’s score on the test. Someone discovers that performance on the test is related to the size of the student’s graduating high school class. The relationship is quadratic:

score = 45.6 + .082 class - .000147 class²,

where class is the number of students in the graduating class.

(i) How do you literally interpret the value 45.6 in the equation? By itself, is it of much interest? Explain.

(ii) From the equation, what is the optimal size of the graduating class (the size that maximizes the test score)? (Round your answer to the nearest integer.) What is the highest achievable test score?

(iii) Sketch a graph that illustrates your solution in part (ii).

(iv) Does it seem likely that score and class would have a deterministic relationship? That is, is it realistic to think that once you know the size of a student’s graduating class you know, with certainty, his or her test score? Explain.