The mathematical expression that represents the logistic growth in a population is:

$\frac{dN}{dt}=rN(\frac{K-N}{K})$

The correct answer is Option (2) → $\frac{dN}{dt}=rN(\frac{K-N}{K})$

Logistic growth: A population growing in a habitat with limited resources show initially a lag phase, followed by phases of acceleration and deceleration and finally an asymptote, when the population density reaches the carrying capacity. A plot of N in relation to time (t) results in a sigmoid curve. This type of population growth is called Verhulst-Pearl Logistic Growth. yeast is an example of logistic growth curve and is described by the following equation:

 \(\frac{dN}{dt}\) = rN(\(\frac{K-N}{K}\))

Where N = Population density at time t, r = Intrinsic rate of natural increase, K = Carrying capacity.

Logistic growth occurs when there is a fixed carrying capacity, meaning that the environment has a limited capacity to support a population. In this type of growth, the population initially experiences exponential growth, but as it approaches the carrying capacity, the growth rate slows down and eventually levels off. The carrying capacity represents the maximum population size that the environment can sustain with its available resources.