Examples o growth and decay in differential equation?

Answer 1

In differential equations, growth can be exemplified by the logistic growth model, represented by the equation (\frac{dP}{dt} = rP(1 - \frac{P}{K})), where (P) is the population, (r) is the growth rate, and (K) is the carrying capacity. Conversely, decay is illustrated by the exponential decay model, given by (\frac{dN}{dt} = -\lambda N), where (N) is the quantity and (\lambda) is the decay constant. These models describe how populations grow towards a limit or decline over time, respectively.