The exponential, logistic, and Gompertz models each describe population growth, but they differ in how they handle limitations and growth behavior. Theexponential model represents ideal, unlimited growth where the population increases rapidly without any constraints. Its curve continuously accelerates, meaning the larger the population becomes, the faster it grows. In contrast, the logistic model introduces environmental limits through a carrying capacity K. The population initially grows rapidly like the exponential model, but as resources become limited, growth slows and eventually levels off at K, forming a symmetric S-shaped curve. The Gompertz model is also limited by a carrying capacity, but its growth pattern is asymmetric. It begins with very slow growth, accelerates in the middle phase, and then approaches the carrying capacity more gradually than the logistic model. While exponential growth is suitable for short-term modeling with no limitations, the logistic model is better for populations experiencing competition for resources, and the Gompertz model is useful when early growth is suppressed but later growth increases, such as in tumor growth or certain animal populations.
![The exponential, logistic, and Gompertz models each describe population growth, but they differ in how they handle limitations and growth behavior. Theexponential model represents ideal, unlimited growth where the population increases rapidly without any constraints. Its curve continuously accelerates, meaning the larger the population becomes, the faster it grows. In contrast, the logistic model introduces environmental limits through a carrying capacity [i]K[/i]. The population initially grows rapidly like the exponential model, but as resources become limited, growth slows and eventually levels off at [i]K[/i], forming a symmetric S-shaped curve. The Gompertz model is also limited by a carrying capacity, but its growth pattern is asymmetric. It begins with very slow growth, accelerates in the middle phase, and then approaches the carrying capacity more gradually than the logistic model. While exponential growth is suitable for short-term modeling with no limitations, the logistic model is better for populations experiencing competition for resources, and the Gompertz model is useful when early growth is suppressed but later growth increases, such as in tumor growth or certain animal populations.](https://www.geogebra.org/resource/rukxcek3/I3Rc5EyXa6k4Lehg/material-rukxcek3.png)