Students will investigate the graphs of logistic functions, function characteristics, and solving logistic equations in Problem 1.
Application problems that are modeled by logistic functions are completed in Problem 2-4. This activity is appropriate for Algebra II or Precalculus.
Before the Activity
This investigation usually follows the study of exponential and power functions. The logistic function is characterized by an elongated s curve, where we start with an increasing growth rate and after the point of maximum growth we view a decreasing rate. The activity also includes solving logarithmic equations and application problems.
The teacher should review basic equation solving process and also solving logarithmic equations, that is, taking the log of each side and solving for x.
During the Activity
This activity is designed to be student-centered. The teacher may act as a facilitator while students work independently or cooperatively. The teacher will inform students in which manner they are to work.
The ready-to-use worksheet will provide a written assignment which can be used for daily credit points.
The file titled logistic function SOL shows the expected results of working through the activity and the screenshots are included in the step-by-step instructions.
After the Activity
Students may select logistic problem examples from internet sites and bring them in and post them for other students to complete for extra credit/ present the problem to the class.
Students could complete a science/math project growing some seedling over a few week period, recording growth, use non-growing lamps vs. growth lamps conditions, fertilizer vs. no fertilizer or different kinds, etc.