A total population P(t) can be partitioned into the sum of all young people Y(t), all of the middle- aged M(t), and all old people O(t). In other words, the total population can be written as P(t) = Y(t) + M(t) +O(t). The growth rate of the young population is ry, that of the middle-aged is M, and the growth rate of the old population is ro. Show that the growth rate of the total population rp (t) is a weighted sum of the growth rates ry, M, and ro. What are the weights? Carefully explain your work.