Biology · Organisms and Populations · NEET
| Resource assumption | Unlimited food and space | Limited (finite) resources |
| Curve shape | J-shaped | S-shaped (sigmoid) |
| Equation | dN/dt = rN; Nt = N0e^rt | dN/dt = rN[(K-N)/K] |
| Carrying capacity (K) | Not present / not applied | Central; growth stops at N = K |
| Does growth stop? | No, keeps rising | Yes, at asymptote (N = K) |
| Realistic in nature? | No (ideal case only) | Yes (NCERT: more realistic) |
Logistic growth is more realistic. NCERT states: since resources for growth for most animal populations are finite and become limiting sooner or later, the logistic growth model is considered a more realistic one. In nature no habitat has unlimited food and space, so a population cannot grow forever the way the exponential model predicts. This one line is a very common NEET Assertion-Reason question, so learn it word for word.
In exponential growth resources are unlimited, so the growth rate keeps increasing and the curve rises steeply with no ceiling, forming a J. In logistic growth resources are limited, so the population first rises (lag then acceleration), then slows (deceleration) as it nears carrying capacity K, and finally flattens at an asymptote. This lag, acceleration, deceleration and asymptote together bend the curve into an S (sigmoid) shape.
No. The exponential equation is dN/dt = rN (integral form Nt = N0e^rt) and it has no K term, because it assumes resources never run out. K appears only in the logistic equation dN/dt = rN[(K-N)/K]. The presence or absence of K is the fastest way to tell the two equations apart in an exam.
An exponentially growing population never stops on its own, because there is no limiting factor in the model. A logistically growing population stops when N = K, that is when N/K = 1, so the term (K-N)/K becomes zero and dN/dt = 0. At this point the curve reaches its asymptote.
Yes. Both dN/dt = rN and dN/dt = rN[(K-N)/K] use r, the intrinsic rate of natural increase, where r = b - d (per capita birth rate minus per capita death rate). The difference is that logistic growth multiplies r by the extra factor (K-N)/K, which shrinks the effective growth as N approaches K.
Assertion A: The logistic growth model of populations is considered more realistic than the exponential growth model. Reason R: Resources are finite. Choose the most appropriate answer:
Asymptote in a logistic growth curve is obtained when:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Exponential growth assumes unlimited resources and gives an unlimited J-shaped curve, while logistic growth assumes limited resources and gives an S-shaped curve that levels off at carrying capacity K.
The logistic model. NCERT states it is more realistic because resources in nature are finite and become limiting sooner or later.
Exponential: dN/dt = rN, integral form Nt = N0e^rt. Logistic: dN/dt = rN[(K-N)/K]. Only the logistic equation contains carrying capacity K.
Exponential growth gives a J-shaped curve; logistic growth gives an S-shaped (sigmoid) curve with lag, acceleration, deceleration and asymptote phases.
When N equals K (N/K = 1), the factor (K-N)/K becomes zero, so dN/dt = 0 and growth stops at the asymptote.
