Modeling Logistic Growth: Apply It 1

  • Create a logistic growth model to describe a real-world situation that follows a logistic pattern
  • Evaluate a logistic growth model to determine if it accurately represents a situation
  • Use a logistic growth model to make predictions or solve problems related to the growth of a population or system

Understanding and Applying Logistic Growth Models

In this Apply It section, we embark on a journey through the world of logistic growth models, a vital tool for understanding growth patterns in constrained environments. From the population dynamics in aquatic ecosystems to the adoption rates of new technologies and urban population growth, each scenario will challenge you to apply your knowledge of logistic growth models. These exercises are designed to enhance your ability to write, evaluate, and solve logistic growth equations, providing you with a deeper insight into how populations and trends evolve within finite limits.

Scenario 1: Aquatic Ecosystem Fish Population

A biologist is studying a fish population in an aquatic ecosystem. The population growth is observed to follow a logistic model due to limited resources and space.

Having explored the application of logistic models in a natural setting with fish populations, we now turn our attention to the realm of technology. In this next scenario, the focus shifts to understanding how logistic growth models can be applied to the adoption rates of new technological products, illustrating the versatility of these models in both natural and manufactured environments.

Scenario 2: Technology Adoption Rate

A company has released a new technology product, and its adoption over time is being studied. The adoption rate initially grows rapidly but then slows as it approaches market saturation.