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”.


Nt = N0 ert


Nt − Population density at time t

N0 − 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.


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