The exponential growth equation dN/dt expresses the rate of population growth as the per capita rate of increase, r times population size N. This exponential model of population growth can be modified to produce a model in which population growth is sigmoidal by adding an element that slows growth, as population size approaches carrying capacity, K. If the per capita rate of increase rmax is the maximum per capita rate of increase, then select the correct option for the logistic equation for population growth.
1
\(\rm \frac{dN}{dt} = r_{max}\frac{(K-N)}{K}\)
2
\(\rm \frac{dN}{dt} = r_{max}N\frac{(K-N)}{K}\)
3
\(\rm \frac{dN}{dt} = r_{max}\frac{N}{K}\)
4
\(\rm \frac{dN}{dt} = r_{max}\frac{K}{N}\)