Practice question

Geometric growth describes population change in discrete steps, such as breeding seasons or annual censuses. If λ is the finite multiplication factor per step, then N(t+1) = λN(t), and repeated multiplication gives Nt = N0λ^t. The exponent t counts discrete intervals, so a population with λ = 1.2 becomes 1.2 times its previous size at every step. By contrast, Nt = N0e^(rt) is the integrated form of continuous exponential growth, and dN/dt = rN is its differential equation. The two formulations are related by λ = e^r, or r = ln λ, when they refer to equal time units. Net reproductive rate R0 can act as a generation-to-generation multiplier in simplified generation-based models, but it is not generally b − d. Geometric growth is especially suitable when reproduction is synchronized and generations or censuses are separated. Its multiplicative nature creates an accelerating, J-shaped trajectory when λ exceeds 1, even though change is applied at distinct time points.