Question

The equation ${{dN = }}{{{r}}_{{m}}}{{N}}$, (the law of population growth) given by French mathematician, P.F. Verhulst suggest the rate of increase of population per unit time depends upon
A. Innate capacity for increase
B. Population size
C. Unutilized opportunity for population growth
D. All of the above

Answer 1

Pierre Franois Verhulst was born on 28 October 1804 in the city of Brussels. He was a French mathematician. He was also a doctor in number theory from the University of Ghent in 1825 and is best known for the logistic growth model.

Complete answer:
Pierre F. Verhulst was a French mathematician. He was also a doctor in number theory from the University of Ghent in 1825. He introduced his Logistic equation in the year 1838.
His equation was also known as the law of population growth and the equation was $\dfrac{{{{dN}}}}{{{{dt}}}} = {{rN}}\left( {1 - \dfrac{{{N}}}{{{K}}}} \right)$. In the equation, ‘N’ represents the number of individuals at a time period denoted by ‘t’ and ‘r’ is the intrinsic growth rate and K denotes the carrying capacity or the maximum number of individuals that can support the environment.
In a journal, which was introduced in the year 1845, he explained this solution as the logistic function, and the equation is now known as the logistic equation. This model was redescribed by Raymond Pearl and Lowell Reed in 1920 and they promoted the use of this equation.
Biotic potential explains the rate at which a population of a given species will increase when there are no limits of any sort on its rate of growth. It is this rate of population growth that was derived by the formula $\dfrac{dN}{dt} = rN\left(1-\dfrac{N}{K}\right)$.
Here N refers to the number of individuals in the population and $\dfrac{dN}{dt}$ refers to the rate of change of its numbers over time. In this equation, r is the intrinsic rate of natural increase for the population.

Hence, the correct answer is option (D).

Additional information:
Population growth refers to the increasing number of individuals in a population. Recent journals show that the global human population growth rate is around 83 million annually. In the year 1800, the global population was 1 billion which has grown to 7.8 billion in 2020. In different countries, the rapid population growth causes low standards of living On the other hand many nations with low rates of population growth have high standards of living.

Note: The equation of law of population growth was prescribed by Pierre F. Verhulst in the year 1845. He was a French mathematician and a doctor in number theory from the University of Ghent. His equation was $\dfrac{dN}{dt} = {rN}$ where N denotes the number of individuals in the population and $\dfrac{dN}{dt}$ refers to the rate of change of its numbers over time, and r is the intrinsic rate of natural increase for the population.