Question

the model of population growth assumes that the rate of growth is proportional to both the population size and the availability of resources.

Explanation:

The logistic model of population growth accounts for the fact that as population size increases, resources become limited. The growth rate is proportional to the population size (indicating that more individuals can reproduce) and also to the amount of available resources (since limited resources will slow growth). Mathematically, the logistic differential equation is \(\frac{dP}{dt}=rP(1 - \frac{P}{K})\), where \(P\) is the population size, \(r\) is the intrinsic growth rate, and \(K\) is the carrying capacity (maximum population size that the environment can support). The term \((1-\frac{P}{K})\) represents the availability of resources (when \(P = K\), \((1-\frac{P}{K})=0\) and growth stops; when \(P\ll K\), \((1 - \frac{P}{K})\approx1\) and growth is close to exponential, \(rP\)).

Answer:

logistic