Read the following two mathematical equations for population growth: (i) dN dt = rN (ii) dN dt = rN ( K-N K ) What are the respective shapes of the population growth curves produced by these equations when population density ( N ) is plotted against time ( t )?

Step-by-step solution

Equation (i) dN dt = rN describes exponential growth, which occurs when resources in the habitat are unlimited. When population density ( N ) is plotted against time ( t ) for this equation, it results in a J-shaped curve. Equation (ii) dN dt = rN ( K-N K ) represents the Verhulst-Pearl logistic growth model, which occurs when resources are limited. Plotting N against t for this equation yields a Sigmoid (S-shaped) curve. Answer: (i) J-shaped curve, (ii) Sigmoid curve