examples of logistic and exponential population growth
Growth Models

Exponential Growth − When the resources are unlimited, population tends to grow in an exponential pattern.

If the population size is N and the birth and death rates (not per capita) are b and d respectively, then increase or decrease in N at t (time period) is given by,

dN /dt = (b − d) × N
If (b − d) = r, then
dN/ dt = rN
r is the “intrinsic rate of natural increase”.
Or,
N_{t} = N_{0} e^{rt}
Where,
N_{t} − Population density at time t
N_{0} − Population density at time 0
r − Intrinsic rate of natural increase
e − Base of natural logarithms (2.71828)
eg. Bacteria grown in lab is the best example to this

Logistic growth − When the resources are limited leading to competition between individuals and survival of the fittest, the population tends to grow in a logistic manner.

In this kind of growth, there is an initial lag phase followed by acceleration or deceleration phases and finally asymptote, when it reaches its carrying capacity (K).

When N in relation to t is plotted, it results in a sigmoid curve called the Verhulst − Pearl Logistic growth given by,

N − Population density at time t
r − Intrinsic rate of natural increase
K − Carrying capacity
eg yeast , fungus used in beverages and break making is an example of logistuc curve.
Regards