For my mathematical exploration in SL, I chose to model the carrying capacity of the earth. Carrying capacity is a variable that denotes the number of people, other living organisms, or crops a region can support without environmental degradation. In this exploration, I will use several mathematical models to explore the growth rate of a population and at what point the population reaches the carrying capacity of the earth. Reproduction is proportional to the number of individuals. In exponential growth, 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 Shouldn't Be Banned"? Get Original EssayHowever, 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. Based on the amount of food, space, water, and other essentials available, an environment will have a carrying capacity. As a result, when populations reach environmental limits, growth rates decline, and in other cases, even if populations reach environmental limits, the growth rate will not change. In any given environment, there will always be a constraint on the growth of the species living in that environment. As mentioned above, these environmental limitations can be the lack of resources such as food, water, space, etc. These limitations act as a “ceiling” on population growth. Populations can grow and gradually reach a maximum size, or continue to grow without any change in growth rate. To be more concrete, there are 2 different types of population growth: logistic and exponential. These two functions have evidently and thoroughly been verified as the only models for species population growth. Please note: this is just an example. Get a custom paper from our expert writers now. Get a Custom Essay In nature, populations start growing rapidly and exponentially however, due to environmental restrictions, they are limited. Although the following reasons are only fatal and have no relation to carrying capacity, the growth rate of a population may also slow down due to declining fertility and birth rates, increased mortality due to lack of healthcare, 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, known as the carrying capacity. The variable "K" represents the carrying capacity.