Modeling Using Logistic Growth
The purpose of this lesson plan is to teach students about logistic growth functions through real-world applications like mold growth, enabling them to model, interpret, and apply these functions to various scenarios. Students will observe mold growth patterns, create logistic models using a DESMOS interactive activity, and learn to identify and interpret key parameters of logistic growth functions within the context of real-world problems.
Overview
Students begin with a gallery walk of five mold images, recording an observation and a question at each, then discuss why growth should level off rather than continue exponentially. In Desmos, groups select four of ten data sets on mold growth on building materials, fit a logistic function with sliders, record the equations, predict values, and research how humidity and temperature affect growth. A 3Blue1Brown video on modeling COVID-19 spread, guided notes on carrying capacity, growth rate, and initial condition, and practice problems follow. Students then plot two new data sets, build a model by hand, and compare it with a logistic regression. A choice-board exit ticket assesses understanding. Phases should take approximately 8 to 45 minutes each, with the whole lesson taking two to three days.
Lesson Objectives
- Explain the difference between logistic growth and exponential growth functions
- Identify and interpret key parameters of logistic growth (carrying capacity, c; growth rate, k; initial condition, B) within the context of a problem
- Evaluate logistic growth functions
- Create logistic growth equations (models) from word problems and data
- Apply logistic growth models to explain real-world scenarios
Standards
NGSS · 3
- HS-LS2-1Use mathematical and/or computational representations to support explanations of factors that affect carrying capacity of ecosystems at different scales.
- HS-LS2-2Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales.
- HS-LS2-6Evaluate the claims, evidence, and reasoning that the complex interactions in ecosystems maintain relatively consistent numbers and types of organisms in stable conditions, but changing conditions may result in a new ecosystem.
CCSS Math · 4
- MP4Model with mathematics. Students will apply mathematical models to solve problems arising in everyday life, society, and the workplace.
- HSF-IF.B.4For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Focus on increasing/decreasing intervals, asymptotes, and maximums/minimums in the context of population).
- HSS-ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- HSS-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. (Specifically, students will consider the logistic function as a fit).