We can see that the result is dependent on the initial condition N 0 as well as the growth rate k . In 1798 Thomas Mathus pointed out that populations can't grow indefinitely, but must at some point become resource limited. This was latter expanded by Darwin as part of the theory of evolution. One approach is the monomolecular growth curve, used to describe the increase in concentration of a product formed from a first-order chemical reaction. It has also been used to describe nutrient uptake by a cell in a constant medium.
P is the product.
The logistic growth equation is similar to exponential growth but includes an additional density-dependent term, which limits the rate of growth as the population approaches a maximum size, termed the carrying capacity . The model assumes that the relative growth rate declines linearly with population size . The logistic growth equation assumes that the relative growth rate decreases with the population size instantaneously. Often, there is rather some delay in the effects of the population size on relative growth. The logistic growth equation can be expressed in discrete , and opposed to continuous time.