Question

The growth curve observed in a population growing under limited resources is:

• A. J-shaped curve
• B. S-shaped curve
• C. Zig-zag curve
• D. Bell-shaped curve

Hint:

Remember: \[ \text{Exponential growth} \rightarrow \text{J-shape} \] \[ \text{Logistic growth} \rightarrow \text{S-shape} \] Carrying capacity (\(K\)) limits population growth.

Answer 1

The Correct Option is B

Concept: Population growth under resource limitation follows the logistic growth model. The logistic growth equation is: \[ \frac{dN}{dt}=rN\left(\frac{K-N}{K}\right) \] where: \[ N = \text{Population density} \] \[ r = \text{Intrinsic rate of increase} \] \[ K = \text{Carrying capacity} \]

Step 1: Understand unlimited resource growth. When resources are unlimited, population increases exponentially and forms a: \[ \text{J-shaped curve} \]

Step 2: Understand limited resource growth. When resources become limited:

• Population growth slows down
• Competition increases
• Population stabilizes near carrying capacity

This produces an: \[ \text{S-shaped (sigmoid) curve} \] Therefore, the correct answer is: \[ \boxed{\text{S-shaped curve}} \]