What does ‘r’ denote in the given equation?dN/dt = rN

The correct answer is Option (4) → Intrinsic rate of natural increase

The equation dN/dt = rN describes exponential growth, when resources are unlimited. Here N is the population size and dN/dt its change per unit time. r is the birth rate minus the death rate, per individual (r = b − d). It is an important measure of how a population responds to any biotic or abiotic factor.

Option (1) Population density — Incorrect. Population size or density is N in the equation.

Option (2) Time — Incorrect. Time is t. dN/dt is the change in population size per unit time, so time is in the denominator, not in r.

Option (3) Base of natural logarithms — Incorrect. That is e, which appears in the integral form N_t = N₀e^rt, not as r.

Option (4) Intrinsic rate of natural increase — Correct. In exponential growth, dN/dt = rN, r is the intrinsic rate of natural increase, birth rate minus death rate per individual. It measures the effect of biotic or abiotic factors on population growth.

Note: A similar question was also asked in CUET (UG) 2025 on 13-05-2025 (Slot 2).

NCERT Extract:
Population Growth – “… Ideally, when resources in the habitat are unlimited, each species has the ability to realise fully its innate potential to grow in number, as Darwin observed while developing his theory of natural selection. Then the population grows in an exponential or geometric fashion. If in a population of size N, the birth rates (not total number but per capita births) are represented as b and death rates (again, per capita death rates) as d, then the increase or decrease in N during a unit time period t (dN/dt) will be
dN/dt = (b – d) × N
Let (b–d) = r, then
dN/dt = rN
The r in this equation is called the ‘intrinsic rate of natural increase’ and is a very important parameter chosen for assessing impacts of any biotic or abiotic factor on population growth.”