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Difference Between Exponential Growth and Logistic Growth

Exponential Growth vs Logistic Growth

The difference between exponential growth and logistic growth can be seen in terms of the growth of population. Population growth is defined as an increase in the size of a population over a specific time period. The growth rate is calculated using two factors – the number of people and the unit of time. This rate is influenced by the rate at which birth takes place every year (also known as the birth rate). It is also influenced by the rate at which living beings die (also known as the death rate).

The size of the population does not rise indefinitely because of the limitation of certain factors. These factors are water and nutrients, space and light as well as the existence of competitors. The explanation for population growth can be done using 2 growth models – the exponential growth and the logistic growth.

Exponential growth and logistic growth are terms which are used in relation to population. The former is the kind of growth which is present when the rate of growth is proportional to amounts which exist. It is same for the latter; however, logistic growth considers other major factors. These are competition and limited resources.

Exponential growth requires specific ideal conditions. These conditions vary to a great extent. In logistic growth, the growth rate is quick at the beginning then it begins to slow down later on. This happens when a number of organisms are in competition for limited space. As the population comes to a state of equilibrium, then the growth rate is equal to zero. Also if there is no interruption, then the population remains stationary. A population has the potential to grow exponentially when it has access to different and unlimited resources. Logistic growth starts rapidly while exponential growth is the opposite. It begins at a slow rate then the rate speeds up when the population rises.

What makes Exponential Growth Different from Logistic Growth?

Exponential growth and Logistic growth models help in explaining the growth of population. Exponential growth is a growth in population wherein the number of individuals increases. This happens even when the rate of growth does not change. As a result, it creates an explosion of the population. Logistic growth entails exponential growth in population along with a growth rate which is in a constant state. As the population comes to its carrying capacity, the growth rate then decreases significantly. This happens due to the availability of limited resources for each and every entity.

  • Exponential Growth

In exponential growth, the sole determining factor for the growth rate of a specific population is the rate of birth. The factor which limits this growth is the availability of resources. When plotting the number of entities against time, the result shows a curve with a J-shaped characteristic. This is the exponential growth.

Based on this curve, the beginning of the growth is slow and it speeds up as the size of the population grows. When looking at the reality, as the population increases in size, then the food supply, as well as space, becomes more and more limited. That is why this model of growth is known to be more idealistic than the logistic growth model.

The most important aspect of exponential growth is the number of entities which come into each generation (otherwise known as the growth rate). It rapidly increases as the population increases in size too. When this happens, then the outcomes can be very dramatic.

  • Logistic Growth

In logistic growth, carrying capacity is taken into account. Carrying capacity is defined as the size in which a specific population ultimately reaches stabilization. When this happens, the population’s growth rate fluctuates. It either goes a bit above or a bit below the carrying capacity. The logistic growth model is more realistic than the exponential growth model. Therefore it is applicable to more kinds of populations which exist on this planet.

When plotting a graph for logistic growth, you will notice that it forms an S-shaped curve. When there are only a few entities, the population will increase in size slowly. Then as the number of entities increase, the population grows in size more rapidly. As a final step, when there are already many entities in the population, the growth then slows down once again. This is because of the limitation of resources and space. In logistic growth, a specific population will keep on growing until it comes to the carrying capacity. This is the maximum quantity of entities which can be supported by the environment.

Common Differences between exponential growth and logistic growth

Both exponential growth and logistic growth are terms which describe models. These models are used to explain population growth effectively. Both models refer to the population but in different ways.

One major difference is that exponential growth starts slow then picks up as the population increases while logistic growth starts rapidly, then slows down after reaching the carrying capacity.

Here are the Differences:

Difference in

Exponential Growth

Logistic Growth

Definition Involves the growth of population over time, taking carrying capacity into account. Involves the growth of population over time, not taking carrying capacity into account.
What it’s also known as J-shaped growth Sigmoid growth
When it occurs When the resources are plentiful When the resources are limited
Stationary phase Stationary phase is not frequently reached. Stationary phase is reached
Number and kinds of phases Only have two phases, namely:

– lag

– log

Has four phases, namely:

– lag

– log

– deceleration

– stationary

Population crash It ultimately crashes.

This is because of mass mortality.

It very rarely crashes.
Commonality Not very common. More common.

Other Differences

  • The exponential growth model shows a characteristic curve which is J-shaped while the logistic grown model shows a characteristic curve which is S-shaped.

  • The exponential growth model is applicable to any population which doesn’t have a limit for growth. The logistic growth model is applicable to any population which comes to a carrying capacity.

  • The exponential growth model typically results in an explosion of the population. The logistic growth model results in a relatively constant rate of population growth. This happens when the growth rate of the population arrives at its carrying capacity.

  • Exponential growth is ideal for populations that have unlimited resources and space – such as bacterial cultures. Logistic growth is more realistic and can be applied to different populations which exist in the planet.

  • The exponential growth model doesn’t have any upper limit. The logistic growth model has and upper limit, which is the carrying capacity.

  • Exponential growth happens when the rate of growth is in proportion to the existing amounts. This is also true for logistic growth but the difference is, it also includes competition and resources which are limited.

Summary

  • Population growth can be explained easier using exponential growth and logistic growth. One is different from the other in terms of how they work and how they are defined. Also, the former model involves unlimited resources while the latter model doesn’t. So the results of both kinds of growth are vastly different too.

  • Exponential growth occurs when the birth rate in a specific time period is continuous. This birth rate isn’t hindered because of limited resources. A good example to show this is bacteria cultures. A single bacterium divides into two. These two bacteria’s then divide, resulting in 4, then 8, then 16 and so on. The process of dividing will keep on continuing until resources become limited.

  • Logistic growth occurs when the population rapidly increases in size until it reaches a certain point, called the carrying capacity. At this time, the resources are not enough to support the population. When the population arrives at the upper limit, the environment can no longer support the population so the rate of increase slows down.

  • In exponential growth, the upper limit doesn’t exist and so the population just keeps on growing. In logistic growth, the growth is not continuous. That is why logistic growth is more realistic than exponential growth. In exponential growth, the rate at the beginning is slow but then it gains momentum as the size of the population increases. In logistic growth, the rate is fast at the beginning then slows down eventually because many entities are competing for the same space and resources.

  • When there is a continuous rate of birth, because there are no factors to hinder it, then exponential growth occurs. Here, the growth rate of individual entities remains constant, no matter what the size of the population is. This is why the growth rate of the population becomes rapid as the size of the population increases. In logistic growth, the growth rate of individual entities reduces and the size of the population increases.


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2 Comments

  1. It was horrible but I still got what I sorta needed

  2. What is the mathematical expression for geometric grouth?

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