Practice question

Continuous exponential growth states that the instantaneous change in abundance is proportional to the abundance already present: dN/dt = rN. Here dN/dt is the population’s absolute rate of change, N is current size, and r is the instantaneous per-capita growth rate. Dividing both sides by N shows that (1/N)(dN/dt) = r, so every individual contributes the same expected net rate under the model. Integration produces Nt = N0e^(rt), demonstrating that the differential and integrated forms describe the same process. Expressions involving λ or a generation multiplier represent discrete geometric growth rather than the continuous formulation. Writing Nt = rN is dimensionally and conceptually incomplete because it relates a population size directly to a rate expression without time integration. Exponential growth predicts accelerating absolute increase when r is positive, stability when r is zero, and exponential decline when r is negative. Its assumptions include constant demographic rates, no density dependence, and an environment that does not impose limiting feedback during the modeled period.