A retail store sells a certain product at the rate of g(t) units per week at time t, where g(t) = rt. At time t = 0, the store has Q units of the product in inventory.

(a) Find a formula f (t) for the amount of product in inventory at time t.

(b) Determine the value of r in part (a) such that the inventory is exhausted in A weeks.

(c) Using f (t), with r as in part (b), find the average inventory level during the period 0 ≤ t ≤ A.