For my SL math exploration, I chose to model the carrying capacity of the Earth. Carrying capacity is a variable that indicates the number of people, other living organisms, or crops that a region can support without environmental degradation. In this exploration, I will use different mathematical models to explore the growth rate of a population and when the population reaches the carrying capacity of the Earth. Reproduction is proportional to the number of individuals. Growing exponentially, the population grows faster and faster, continuing to double in size at regular intervals. Exponential growth can be a good model for early-stage populations such as bacteria. Say no to plagiarism. Get a tailor-made essay on “Why Violent Video Games Should Not Be Banned”? Get the original essay However, the exponential cannot continue for long for a population to reach a huge value. Exponential growth cannot continue for long because the environment in which the population lives cannot support an infinite population of species. Depending on the amount of food, space, water, and other essentials available, an environment will have a carrying capacity. As a result, as populations reach environmental limits, growth rates decrease, and in other cases, even if the population reaches environmental limits, the growth rate will not change. In a given environment, there will always be a constraint. on the growth of species that live in this environment. As mentioned earlier, these environmental limitations may be due to lack of resources such as food, water, space, etc. These limitations act as a “ceiling” to population growth. Populations can grow and gradually reach a maximum size, or they will continue to grow with no change in growth rate. To be more concrete, there are 2 different types of population growth: logistic and exponential. These two functions have been verified clearly and precisely as the only models of population growth of the species. Keep in mind: this is just a sample. Get a personalized article from our expert writers now. Get a Custom Essay In nature, populations initially grow rapidly and but exponentially, due to environmental restrictions, they are limited. Although the following reasons are only fatal and have nothing to do with carrying capacity, the growth rate of a population can also slow down due to declining fertility and birth rates, increased mortality due to lack of health care, violence, disease. , and other natural disasters. In logistic growth, the growth rate decreases as the population approaches a maximum size determined by the environmental context, called carrying capacity. The variable “K” represents the carrying capacity.