Practice question

Net population change from births and deaths is calculated by subtracting losses from gains. During one year, 100 births add individuals and 50 deaths remove them, giving ΔN = 100 − 50 = 50 individuals per year. If these events are treated as rates over that interval, dN/dt is approximated by +50 individuals per year. The initial population of 1,000 is not needed for the absolute change, but it permits calculation of the per-capita rate: r ≈ 50/1,000 = 0.05 per year. Likewise, the per-capita birth and death rates are 0.10 and 0.05 per year, whose difference is 0.05. Multiplying r by N recovers 50. The positive sign matters because births exceed deaths. Immigration and emigration are absent from the information; if present, they would be added through ΔN = B + I − D − E. The calculation is a one-interval estimate and assumes the stated events refer to the same population boundary and time period.