59. Which of the following represents exponential growth in populations?

 

What is Exponential Growth in Populations?

Exponential growth describes how a population increases rapidly when resources are unlimited and environmental conditions are ideal. In this scenario, every individual contributes to the population’s growth, resulting in a rate of increase that is directly proportional to the current population size.

The J-Shaped Curve: Signature of Exponential Growth

When population size is plotted over time under exponential growth conditions, the resulting graph is a J-shaped curve. This curve starts with a slow increase (lag phase), followed by a rapid, accelerating rise as the population multiplies unchecked.

Why a J-Shaped Curve?

• Unlimited Resources: There are no constraints—food, space, and other essentials are abundant.

• Constant Growth Rate: The per capita rate of increase (r) remains constant, so the larger the population, the faster it grows.

• No Carrying Capacity: The environment does not impose a maximum limit on population size.

Mathematical Representation

Exponential growth is described by the equation:

dNdt=rNdtdN=rN

• N = population size

• r = intrinsic rate of increase

• dN/dt = rate of change in population size over time

This formula shows that the rate of population growth is always proportional to the current population size.

Real-World Examples

• Bacteria in a Fresh Medium: Bacteria like E. coli can double every generation, producing a classic J-shaped curve until resources are depleted.

• Invasive Species: Newly introduced species often show exponential growth before environmental limits kick in.

• Rebounding Populations: After a catastrophic decline, populations may grow exponentially if conditions suddenly become favorable.

Exponential vs. Logistic Growth

Key Takeaways

• Exponential growth in populations is best represented by a J-shaped curve.

• This pattern occurs only when resources are unlimited and environmental resistance is absent.

• In nature, exponential growth is typically short-lived, as resources eventually become limiting, leading to logistic (S-shaped) growth.

Conclusion

If you’re looking for the graph that represents exponential growth in populations, choose the J-shaped curve. It’s the hallmark of unchecked, rapid population increase seen under ideal, unlimited conditions—a foundational concept in population ecology.