Question

The formula for exponential population growth is
(A) dN/ rN =dt
(B) rN/dN=dt
(C) dN/dt=rN
(D) dt/dN=rN

Answer 1

Hint: A population shows exponential growth when there is no limitation on growth i.e. in an idealized unlimited environment. Under an ideal unlimited environment, the per capita rate of increase (the number of offspring born per individual) is maximum.

Complete step by step answer:
During exponential growth, the number increases in the geometric progression and in geometric growth, the rate of increase is expressed by a constant factor or an exponent by which a particular population can be multiplied (like 2,4,8,16…….). The exponential form of growth may be represented by the simple model which is based on the exponential equation:-
dN/dt = rN OR dN/dt*1/N =r
Where N is termed as the population size and r is the intrinsic rate of increase. The maximum value of r is often referred to as biotic potential and differs from one species to another e.g deer population can grow faster than a population of elephants.

So, the correct answer is (c) dN/dt =rN

Note:
During an exponential growth when the population growth is under an ideal unlimited environment, the per capita rate of increase is maximum and is called the intrinsic rate of increase and is expressed in number per unit time per unit individual.
The sum total of all environmental factors acting together to limit the biotic potential of an organism from being realized is called environmental resistance. It includes both biotic factors such as predation, competition, parasitism and abiotic factors such as fire, flood etc.