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Mathematics - Other

A group has just been formed with an initial membership of P0. Suppose that the fraction of the membership of the group that remain in the group for at least t years is given by the function S(t), and that at time t, new members are being added to the group at the rate of R(t) members per year. Show that N years from now, the group will contain P(N) members, where P(N) = P0S(N) + integral from N to 0 R(t)S(N - t) dt

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