52. Among the following which follows the populationgrowth pattern according to equation dN/dt=rN whenresources are unlimited

Understanding Exponential Population Growth

Population growth is a fundamental concept in ecology, describing how the number of individuals in a population changes over time. When resources such as food, space, and water are unlimited, populations can grow at their maximum potential rate. This scenario is captured by the exponential growth model, represented by the equation:

dNdt=rNdtdN=rN

Where:

• N = population size

• r = intrinsic rate of natural increase (biotic potential)

• dN/dt = rate of change of the population over time

What Does the Equation Mean?

The equation dNdt=rNdtdN=rN describes a situation where the rate at which the population grows is directly proportional to the current population size. As the population increases, the growth rate accelerates, resulting in a rapid, unchecked rise in numbers. This growth pattern is known as exponential growth.

When Does Exponential Growth Occur?

Exponential growth occurs under ideal conditions:

• Unlimited resources (food, space, shelter)

• No environmental resistance (predators, disease, competition, or limiting factors)

• Maximum reproductive potential for the species

In real ecosystems, such conditions are rare and usually temporary, but they can occur in newly colonized habitats or laboratory settings.

The J-Shaped Curve

Graphically, exponential growth produces a J-shaped curve. This means that as time progresses, the population size increases slowly at first, then more and more rapidly, with no upper limit as long as resources remain unlimited.

Key Features of Exponential Growth

• Rapid Increase: The larger the population gets, the faster it grows.

• No Carrying Capacity: There is no leveling off; the population does not stabilize.

• Short-Lived in Nature: Eventually, resources become limited, and growth slows or stops.

Real-World Examples

• Bacteria in a Petri Dish: When provided with abundant nutrients, bacteria can double in number every few minutes, following an exponential pattern until resources run out.

• Introduced Species: When a species is introduced to a new environment without natural predators or competitors, it may initially grow exponentially.

Exponential vs. Logistic Growth

Why Is Exponential Growth Important?

Understanding exponential growth is essential for:

• Predicting population booms (e.g., pests, invasive species)

• Managing resources and conservation efforts

• Modeling the early stages of population establishment

Conclusion

The population growth pattern that follows the equation dN/dt = rN when resources are unlimited is exponential growth. This model explains how populations can rapidly expand in ideal conditions, producing a J-shaped growth curve. While exponential growth is rarely sustained in nature, it is a foundational concept in ecology and population biology