The following table shows the estimated daily profit from a new product for several of the alternative choices for the production rate.

Production Rate (R)               Profit per Day (P)

0..................................................................0

1..............................................................$ 95

2...............................................................184

3...............................................................255

4...............................................................320

Because the profit goes up less than proportionally with the production rate (decreasing marginal returns), the management science team analyzing what this production rate (and the production rates of some other products) should be has decided to approximate the profit (P) by a simple nonlinear function of the production rate R.

a. One such approximation is P = $100 R2 $5 R2. How closely does this nonlinear function approximate the five values of P given in the table?

b. Repeat part a for the approximation, P = $104 R2 $6 R2.

c. Which of these two nonlinear functions provides the better fit to all the data?