In Problem B of the Qualification Round, you estimated the number of stars in the Milky Way by assuming a constant density of stars throughout the galaxy. However, the density of stars is not constant and varies significantly across different regions. (a) Name the three regions A, B, C marked in the horizontal Milky Way drawing below. A B с Scientists have developed a basic model for the Milky Way to describe the density distribution of stars p(r) at distance from the center by evaluating the three regions A, B, C: + exp Ως RB (ne - Fe)] r Rc P(r) = v A) · [exp (DA - 774) + exp (DB-77) The model parameters have the values below: = 104 stars/(light-year)³ RA = 20 light-years RB 12 103 light-years = Rc 5 10 light-years = ΩΑ = 21, ΩΒ = =3, Ως = -8 (b) Create a double logarithmic plot of the density distribution p(r) with respect to r. (c) Using this model, calculate the number of stars in the Milky Way (r 130,000 light-years). Note: Assume that the Milky Way has a constant thickness of 1,000 light-years.​