Baseball Salaries: Larger or Smaller than Predicted?
The average salary S of a baseball player (in thousands of dollars per year) in year x (with 1982 corresponding to x=0) is given by the model: S = 246 + 64x  8.9x^{2} + 0.95x^{3}.
Task 1: According to this equation, what should be the average salary of a baseball player today (2007)? Do you think this seems right? Explain.
Task 2: Search web sites, trying to find the current average salary for a player. Once you find it, try to explain why the prediction equation is or is not still valid.
Task 3: Consider the web site Baseball Almanac, which shows a graph of average baseball salaries beginning in 1970. Does this graph agree with your data...or the given equation? Is the situation as "exponential" as it looks? Explain.
Task 4: If you were to start from scratch and generate a prediction equation for average salaries, what would you do...and what is your resulting equation?
Source: L. Goldstein's College Algebra and Its Applications, 1993, p. 175
Hint: No hint...just tasks to do.
Solution Commentary: Will depend on your approach, etc.
