Practice question

During exponential growth, doubling time is ln(2)/r. With r = 0.2 per unit time, doubling time is approximately 0.693/0.2 = 3.47 time units. The relation follows by setting N(t)/N(0) = 2 in N(t) = N(0)e^(rt) and solving for t. Parameters have clear roles: N is current abundance, r is the maximum per-capita rate under the model, and K is the positive equilibrium set by environmental capacity. The term 1 - N/K supplies negative feedback. Checking limiting cases at N = 0, N = K, and N far below K is an efficient way to test an interpretation. The decisive distinction is therefore between a descriptive label and the demographic mechanism that generates it. Interpreting the example at the appropriate population scale keeps the causal mechanism distinct from a simple correlation or an absolute rule. Ecological predictions remain conditional on the stated environment, because changing resources, mortality, or interactions can alter the observed demographic pattern.