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**Which part of the graph shows an exponential growth of population?** In principle, any sort of creature might take over the Earth by simply reproducing at an uncontrollable rate. Imagine, for the sake of this illustration, that we began with a single pair consisting of male and female rabbits. If these rabbits and all of their offspring were to continue having offspring at a rapid rate (“like bunnies”) for the next 777 years without any of them passing away, we would have enough rabbits to populate the whole state of Rhode Island.

You’ve undoubtedly observed that there isn’t a foot-thick coating of germs covering the whole planet (at least, not at my place), and that rabbits haven’t taken over Rhode Island. If this is the case, then why don’t we see these populations growing to the levels that they are capable of in theory? In order to live and reproduce, E. coli, like rabbits and all other living beings, need particular resources, such as nutrition and conditions that are conducive to their growth. These resources are not limitless, and a population can only grow to a level that is proportional to the amount of resources that are readily available in its immediate area.

Ecologists that study populations simulate the movement of populations using a wide range of mathematical techniques (how populations change in size and composition over time). Some of these models depict development in an unrestricted environment, while others include “ceilings” that are contingent on the availability of finite resources. It is possible to utilize mathematical models of populations to precisely characterize the changes that are taking place in a population and, more crucially, to anticipate the changes that will take place in the future.

In the two basic models of population growth, the rate of change in the size of a population over the course of time is described by deterministic equations, which are equations that do not take into account the occurrence of random events. The first of these models, known as exponential growth, is used to describe hypothetical populations that continue to expand in size without hitting any kind of ceiling on their expansion. The second model, known as logistic growth, assumes that reproductive growth is subject to restrictions that become more stringent as the size of the population grows. Both models fall short of providing an accurate description of natural populations, but they do provide useful points of comparison.

The development of bacteria in the laboratory is a great illustration of the exponential growth model. The growth rate of a population that is experiencing exponential expansion grows over the course of time and is directly proportional to the size of the population.

Let’s have a look at the mechanics behind this, shall we? Bacteria reproduce by a process known as binary fission, which literally translates to “splitting in half,” and the amount of time that passes in between divisions for the majority of bacterial species is around an hour. To have a better understanding of how exponential growth works, let’s begin by putting one thousand bacteria in a flask that has an infinite supply of nutrients.

After one hour, every bacterium will have produced 2000 new bacteria due to the process of division (an increase of 1000 bacteria).

After two hours, every one of the 2,000 bacteria will split, resulting in the production of 4,000 new bacteria (an increase of 2000 bacteria).

After three hours, each of the 4,000 bacteria will split, resulting in the production of 8,000 new bacteria (an increase of 4000 bacteria).

The fundamental idea behind exponential growth is that the population growth rate, or the number of organisms that are added to the population with each new generation, steadily accelerates as the population continues to expand. And the consequences may be rather dramatic: after only one day (24 cycles of division), our bacterial population would have increased from one thousand to over sixteen billion. A growth curve in the form of a J is produced when the size of the population, N, is plotted against time.

Since exponential development is dependent on an unending supply of resources, this state of things is not particularly conducive to a sustainable future (which tend not to exist in the real world).

If there are a small number of people but a large amount of resources, exponential growth may occur over a period of time. However, when there are a sufficient number of people in a population, resources begin to be used up, which slows down the growth rate. The rate of growth will eventually reach a plateau, at which point an S-shaped curve will be produced. The carrying capacity, abbreviated as K, is the population size at which it reaches a plateau and defines the maximum population size that a specific ecosystem is capable of supporting.

In general, a limit may be almost any form of resource that is significant to the survival of a species. The water, sunshine, and nutrients, as well as the area for the plant to expand into, are some of the most important resources. Important resources for animals include food, water, a safe place to nest, and protection from the elements. Competition for these few resources occurs among members of the same population; this kind of competition is known as intraspecific competition (intra- means inside, and -specific refers to the species).

It is possible that intraspecific rivalry for resources will not effect populations that are much below their carrying capacity since there is an abundance of resources and every person can receive what they need. However, as the number of people in a population grows, the level of competition rises. Furthermore, the buildup of waste products has the potential to lessen the carrying capacity of an ecosystem.

It is termed a J-shaped curve because the graph of exponential growth looks like the letter J. Along this curve, the population grows somewhat slowly at first, but subsequently it accelerates. As long as there is a continuing supply of resources, almost every population will continue to expand at an exponential rate.

As a population approaches a maximum that can be sustained by the limiting resources in its environment, often known as the carrying capacity, the logistic growth model predicts that the per capita growth rate of that population would gradually decrease ( K). Growth at an exponential rate results in a J-shaped curve, whereas growth at a logistic rate results in an S-shaped curve.

When a population is in the exponential growth phase of its growth cycle, the size of the population doubles at each time interval.

Another way of putting it is that the doubling time of the population, which is the number of years it takes for the population to expand to be twice as large as it was initially, is likewise constant. If the population is expected to double in the next 36 years, and then double again in the 36 years after that, and so on, then its growth is exponential.

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