The Law of Mass Action tells us that the time, T, taken by a chemical to create a quantity x_0 of the product (in molecules) is given by T = int_0ˣ_0 frack dx(a-x)(b-x), where a and b are initial quantities of the two ingredients used to make the product, and k is a positive constant. Suppose 0 < a < b. Find the time taken to make a quantity x_0 = a/2 of the product.