Q. The formula for exponential population growth is:
Solution:
Logarithmic or Exponential phase:
In this phase, there is a rapid increase in population till the food is available, but after the decrease in the availability of food, there is a sudden increase in mortality called population crash. For e.g. Many insect populations show exponential growth and increase in their population size in the rainy season but is followed by a population crash at the end of the rainy season. If in a population of size 'N', the birth rate and death rate are represented as 'b' and 'd' respectively, then change in population size (decrease/increase in the 'N') during a unit time period 't' will be
dN/dt = (b-d) × N
If (b – d) = r, then dN/dt = rNdNdt=rN
Where r = intrinsic rate of natural increase, in exponential growth, if 'N' is plotted as a function of time, the curve becomes J-shaped.
In this phase, there is a rapid increase in population till the food is available, but after the decrease in the availability of food, there is a sudden increase in mortality called population crash. For e.g. Many insect populations show exponential growth and increase in their population size in the rainy season but is followed by a population crash at the end of the rainy season. If in a population of size 'N', the birth rate and death rate are represented as 'b' and 'd' respectively, then change in population size (decrease/increase in the 'N') during a unit time period 't' will be
dN/dt = (b-d) × N
If (b – d) = r, then dN/dt = rN
Where r = intrinsic rate of natural increase, in exponential growth, if 'N' is plotted as a function of time, the curve becomes J-shaped.