Question

A population has unlimited resources and exhibits rapid and sustained population growth. This type of growth would be best described by which one of the following? A. Exponential B. Logistic C. Sigmoidal D. Parabolic E. Inverse

Short answer

A. Exponential

Step-by-step solution

- Understanding the scenario

The population has unlimited resources, meaning there are no constraints like food shortage or space limitation affecting the growth.

- Identifying growth pattern

The rapid and sustained population growth indicates that the population is growing at a constant rate without slowing down over time.

- Analyzing the options

A. Exponential growth refers to a situation where the growth rate of the population is proportional to its current size, leading to rapid increase.B. Logistic growth shows a population growing rapidly initially, then slowing as it approaches carrying capacity.C. Sigmoidal growth is another term for logistic growth.D. Parabolic growth typically involves a situation with initial increase, followed by a decrease.E. Inverse growth would describe a decrease in population over time.

- Choosing the correct option

Given that the population has unlimited resources and exhibits rapid and sustained growth, the best description is 'Exponential' growth.

Key concepts

Exponential Growth

Exponential growth happens when a population's growth rate is directly proportional to its current size. This means that as the population increases, so does its growth rate. The key idea is that the population grows rapidly without any limits. This type of growth is expressed mathematically as: \[ N(t) = N_0 \times e^{rt} \] where:

• \[ N(t) \] is the population size at time \[ t \]


• \[ N_0 \] is the initial population size


• \[ r \] is the growth rate


• \[ e \] is the base of natural logarithms, approximately equal to 2.718

In real-world examples, exponential growth can occur in bacteria populations or during the early stages of human population growth when resources were abundant.

Logistic Growth

Unlike exponential growth, logistic growth takes into account resource limitations. Populations cannot grow indefinitely because there will always be limiting factors like food, space, or other resources. This type of growth is shaped like an S-curve or a sigmoid curve, where the population grows rapidly at first, then growth slows, and eventually stabilizes at a maximum level, known as the carrying capacity.

The logistic growth equation is:
\[ N(t) = \frac{K}{1 + \frac{K - N_0}{N_0} \times e^{-rt}} \] where:

• \[ K \] is the carrying capacity


• \[ N_0 \] is the initial population size


• \[ r \] is the growth rate

This model is more realistic for many organisms since it considers the environmental limits which slow down and eventually halt population growth.

Unlimited Resources

When a population has unlimited resources, it means there are no constraints like food shortages, space limitations, diseases, or predation that could affect its growth. This situation is idealized and rarely occurs in nature for long times. But when it does, it leads to exponential growth.

Key characteristics of unlimited resources:

• Unlimited food and water


• No competition with other organisms


• Ideal living conditions


• Rapid reproduction rates

In these ideal conditions, each new generation is larger than the previous one, leading to a very steep increase in population size over a short period.

Growth Rate

The growth rate is a critical factor in understanding population dynamics. It determines how quickly a population increases or decreases over time. Growth rate (r) can be positive, indicating growth, or negative, indicating decline.

For exponential growth, the growth rate is constant, meaning the population size multiplies over equal intervals of time. However, in logistic growth, the growth rate decreases as the population approaches the carrying capacity.

Factors affecting growth rate include:

• Birth rates


• Death rates


• Immigration and emigration


• Availability of resources


• Environmental conditions

Understanding the growth rate helps predict how a population might change in the future under different conditions.

Carrying Capacity

Carrying capacity (K) is the maximum population size that an environment can sustain indefinitely. Once a population reaches this level, it means that the environmental resources like food, space, and other necessities are being used at the maximum sustainable level.

Key points about carrying capacity:

• It sets a limit to how much a population can grow.


• It varies with environmental changes and resource availability.


• When populations exceed carrying capacity, it can lead to resource depletion, starvation, and a subsequent population decline.

The concept of carrying capacity is crucial in fields like wildlife management, conservation biology, and sustainable development. It helps in planning and maintaining balance in ecosystems and human societies.