In a certain section of the country, the price of large Grade A eggs is currently $2.50 per dozen. Studies indicate that x weeks from now, the price p(x) will be changing at the rate of p'(x) = 0.2 + 0.003x² cents per week.

a. Use integration to find p(x), and then use the graphing utility of your calculator to sketch the graph of p(x). How much will the eggs cost 10 weeks from now?

b. Suppose the rate of change of the price was p'(x) = 0.3 + 0.003x². How does this affect p(x)? Check your conjecture by sketching the new price function on the same screen as the original. Now how much will the eggs cost in 10 weeks?